Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU104AYU105AYU106AYU107AYU108AYUThe graph of y= 3x6 x4 has a vertical asymptote. What is it? (pp. 224-227)True or False If x=3 is a vertical asymptote of a rational function R , then lim x3 | R( x ) |= . (pp. 224-227)The graph of y=tanx is symmetric with respect to the ______ and has vertical asymptotes at ________________.The graph of y=secx is symmetric with respect to the _______ and has vertical asymptotes at _______________.It is easiest to graph y=secx by first sketching the graph of _____. (a) y=sinx (b) y=cosx (c) y=tanx (d) y=cscxTrue or False The graphs of y=tanx,y=cotx,y=secx,andy=cscx each have infinitely many vertical asymptotes.In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. What is the y-intercept of y=tanx ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. What is the y-intercept of y=cotx ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. What is the y-intercept of y=secx ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. What is the y-intercept of y=cscx ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does secx=1 ? For what numbers x does secx=1 ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does cscx=1 ? For what numbers x does cscx=1 ?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does the graph of y=secx have vertical asymptotes?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does the graph of y=cscx have vertical asymptotes?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does the graph of y=tanx have vertical asymptotes?In Problems 7-16, if necessary, refer to the graphs of the functions to answer each question. For What numbers x,2x2 , does the graph of y=cotx have vertical asymptotes?In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3tanxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=2tanxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=4cotxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3cotxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=tan( 2 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=tan( 1 2 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=cot( 1 4 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=cot( 4 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=2secxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y= 1 2 cscxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3cscxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=4secxIn Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=4sec( 1 2 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y= 1 2 csc( 2x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=2csc( x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3sec( 2 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=tan( 1 4 x )+1In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=2cotx1In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=sec( 2 3 x )+2In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=csc( 3 2 x )In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y= 1 2 tan( 1 4 x )2In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3cot( 1 2 x )2In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=2csc( 1 3 x )1In Problems 17-40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y=3sec( 1 4 x )+1In Problems 41-44, find the average rale of change of f from 0 to 6 . f( x )=tanxIn Problems 41-44, find the average rale of change of f from 0 to 6 . f( x )=secxIn Problems 41-44, find the average rale of change of f from 0 to 6 . f( x )=tan( 2x )In Problems 41-44, find the average rale of change of f from 0 to 6 . f( x )=sec( 2x )In Problems 45-48, find ( fg )( x )and( gf )( x ) graph each of these functions. f( x )=tanx g( x )=4xIn Problems 45-48, find ( fg )( x )and( gf )( x ) graph each of these functions. f( x )=2secx g( x )= 1 2 xIn Problems 45-48, find ( fg )( x )and( gf )( x ) graph each of these functions. f( x )=2x g( x )=cotxIn Problems 45-48, find ( fg )( x )and( gf )( x ) graph each of these functions. f( x )= 1 2 x g( x )=2cscxIn Problems 49 and 50, graph each function. f( x )={ tanx0x 2 0x= 2 secx 2 xIn Problems 49 and 50, graph each function. g( x )={ cscx0x 0x= cotxx2Carrying a Ladder around a Corner Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration. (a) Show that the length L of the ladder shown as a function of the angle is L( )=3sec+4csc (b) Graph L=L( ),0 2 (c) For what value of is L the least? (d) What is the length of the longest ladder that can be carried around the corner? Why is this also the least value of L ?A Rotating Beacon Suppose that a fire truck is parked in front of a building as shown in the figure. The beacon light on top of the fire truck is located 10 feet from the wall and has a light on each side. If the beacon light rotates 1 revolution every 2 seconds, then a model for determining the distance d , in feet, that the beacon of light is from point A on the wall after t seconds is given by d( t )=| 10tan( t ) | (a) Graph d( t )=| 10tan( t ) | for 0t2 . (b) For what values of t is the function undefined? Explain what this means in terms of the beam of light on the wall. (c) Fill in the following table. (d) Compute d( 0.1 )d( 0 ) 0.10 , d( 0.2 )d( 0.1 ) 0.20.1 , and so on, for each consecutive value of t . These are called first differences. (e) Interpret the first differences found in part ( d ) . What is happening to the speed of the beam of light as d increases?Exploration Graph y=tanxandy=cot( x+ 2 ) Do you think that tanx=cot( x+ 2 ) ?For the graph of y=Asin( x ) , the number is called the _______ ________.True or False A graphing utility requires only two data points to find the sine function of best fit.3AYUIn Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3sin( 3x )In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=2cos( 3x+ 2 )In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3cos( 2x+ )In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3sin( 2x+ 2 )8AYUIn Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=4sin( x+2 )5In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=2cos( 2x+4 )+4In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3cos( x2 )+5In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=2cos( 2x4 )1In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3sin( 2x+ 2 )In Problems 3-14, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y=3cos( 2x+ 2 )In Problems 15-18, write the equation of a sine function that has the given characteristics. Amplitude:2 Period: Phaseshift: 1 2In Problems 15-18, write the equation of a sine function that has the given characteristics. Amplitude:3 Period: 2 Phaseshift:2In Problems 15-18, write the equation of a sine function that has the given characteristics. Amplitude:3 Period:3 Phaseshift: 1 3In Problems 15-18, write the equation of a sine function that has the given characteristics. Amplitude:2 Period: Phaseshift:2In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=2tan( 4x )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y= 1 2 cot( 2x )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=3csc( 2x 4 )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y= 1 2 sec( 3x )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=cot( 2x+ 2 )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=tan( 3x+ 2 )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=sec( 2x+ )In Problems 19-26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods. y=csc( 1 2 x+ 4 )Alternating Current (ac) Circuits The current I , in amperes, flowing through an ac (alternating current) circuit at time t , in seconds, is I( t )=120sin( 30t 3 )t0 What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods.Alternating Current (ac) Circuits The current I , in amperes, flowing through an ac (alternating current) circuit at time t , in seconds, is I( t )=220sin( 60t 6 )t0 What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods.Hurricanes Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111-130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The following data represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010. (a) Draw a scatter diagram of the data. (b) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.Monthly Temperature The data below represent the average monthly temperatures for Washington, D.C. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the for y=Asin(x)+B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.Monthly Temperature The given data represent the average monthly temperatures for Indianapolis, Indiana. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.Monthly Temperature The following data represent the average monthly temperatures for Baltimore, Maryland. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28, 2015, in Charleston, South Carolina, high tide occurred at 2:12 AM ( hours) and low tide occurred at 8:18 AM ( 8.3 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.27 feet, and the height of the water at low tide was 0.87 foot. (a) Approximately when will the next high tide occur? (b) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (c) Use the function found in part ( b ) to predict the height of the water at 11 AM on March 28, 2015.Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28. 2015, in Sitka, Alaska, high tide occurred at 8:06 AM ( 8.10 hours) and low tide occurred at 2:48 PM ( 14.8 hours). Water heights arc measured as the amounts above or below' the mean lower low water. The height of the water at high tide was 8.13 feet, and the height of the water at low tide was 1.95 feet. (a) Approximately when will the next high tide occur? (b) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (c) Use the function found in part ( b ) to predict the height of the water at 6 PM on March 28, 2015.Hours of Daylight According to the Old Farmer’s Almanac, in Miami. Florida, the number of hours of sunlight on the summer solstice of 2015 was 13.75 , and the number of hours of sunlight on the winter solstice was 10.52 . (a) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (b) Use the function found in part ( a ) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part ( a ) . (d) Look up the number of hours of sunlight for April 1 in the Old Farmer’s Almanac, and compare the actual hours of daylight to the results found in part ( b ) .Hours of Daylight According to the Old Farmer's Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice of 2015 was 15.27 , and the number of hours of sunlight on the winter solstice was 9.07 . (a) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (b) Use the function found in part ( a ) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part ( a ) . (d) Look up the number of hours of sunlight for April 1 in the Old Farmer’s Almanac, and compare the actual hours of daylight to the results found in part ( b ) .Hours of Daylight According to the Old Farmer's Almanac, in Anchorage, Alaska, the number of hours of sunlight on the summer solstice of 2015 was 19.37 , and the number of hours of sunlight on the winter solstice was 5.45 . (a) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (b) Use the function found in part ( a ) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part ( a ) . (d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part ( b ) .Hours of Daylight According to the Old Fanner's Alumnae, in Honolulu, Hawaii, the number of hours of sunlight on the summer solstice of 2015 was 13.42 , and the number of hours of sunlight on the winter solstice was 10.83 . (a) Find a sinusoidal function of the form y=Asin(x)+B that models the data. (b) Use the function found in part ( a ) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part ( a ) . (d) Look up the number of hours of sunlight for April 1 in the Old Fanner's Almanac, and compare the actual hours of daylight to the results found in part ( b ) .39AYUFind an application in your major field that leads to sinusoidal graph. Write an account of your findings.Find the exact value of each expression. Do not use a calculator. sin 1 1find the exact value of each expression. Do not use a calculator. cos 1 0Find the exact value of each expression. Do not use a calculator. tan 1 1Find the exact value of each expression. Do not use a calculator. sin 1 ( 1 2 )Find the exact value of each expression. Do not use a calculator. cos 1 ( 3 2 )Find the exact value of each expression. Do not use a calculator. tan 1 ( 3 )Find the exact value of each expression. Do not use a calculator. sec 1 2Find the exact value of each expression. Do not use a calculator. cot 1 ( 1 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sin 1 ( sin 3 8 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. cos 1 ( cos 3 4 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. tan 1 ( tan 2 3 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. cos 1 ( cos 15 7 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sin 1 [ sin( 8 9 ) ]Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sin( sin 1 0.9 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. cos( cos 1 0.6 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. tan[ tan 1 5 ]Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. cos[ cos 1 ( 1.6 ) ]Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sin 1 ( cos 2 3 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. cos 1 ( tan 3 4 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. tan[ sin 1 ( 3 2 ) ]Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sec( tan 1 3 3 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. sin( cot 1 3 4 )Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator. tan[ sin 1 ( 4 5 ) ]In Problems 24 and 25, find the inverse function f 1 of each function f . Find the range of f and the domain and range of f 1 . f( x )=2sin( 3x ) 6 x 6In Problems 24 and 25, find the inverse function f 1 of each function f . Find the range of f and the domain and range of f 1 . f( x )=cosx+3 0xIn Problems 26 and 27, write each trigonometric expression as an algebraic expression in u . cos( sin 1 u )In Problems 26 and 27, write each trigonometric expression as an algebraic expression in u . tan( csc 1 u )In Problems 28-44, establish each identity. tancot sin 2 = cos 2In Problems 28-44, establish each identity. sin 2 ( 1+ cot 2 )=1In Problems 28-44, establish each identity. 5 cos 2 +3 sin 2 =3+2 cos 2In Problems 28-44, establish each identity. 1cos sin + sin 1cos =2cscIn Problems 28-44, establish each identity. cos cossin = 1 1tanIn Problems 28-44, establish each identity. csc 1+csc = 1sin cos 2In Problems 28-44, establish each identity. cscsin=coscotIn Problems 28-44, establish each identity. 1sin sec = cos 3 1+sinIn Problems 28-44, establish each identity. 12sin sincos =cottanIn Problems 28-44, establish each identity. cos( + ) cossin =cottanIn Problems 28-44, establish each identity. cos( ) coscos =1+tantanIn Problems 28-44, establish each identity. ( 1+cos )tan 2 =sinIn Problems 28-44, establish each identity. 2cotcot( 2 )= cot 2 1In Problems 28-44, establish each identity. 18 sin 2 cos 2 =cos( 4 )In Problems 28-44, establish each identity. sin( 3 )cossincos( 3 ) sin( 2 ) =1In Problems 28-44, establish each identity. sin( 2 )+sin( 4 ) cos( 2 )+cos( 4 ) =tan( 3 )In Problems 28-44, establish each identity. cos( 2 )cos( 4 ) cos( 2 )+cos( 4 ) tantan( 3 )=0In Problems 45-52, find the exact value of each expression. sin 165In Problems 45-52, find the exact value of each expression. tan 105In Problems 45-52, find the exact value of each expression. cos 5 12In Problems 45-52, find the exact value of each expression. sin( 12 )In Problems 45-52, find the exact value of each expression. cos 80 cos 20 +sin 80 sin 20In Problems 45-52, find the exact value of each expression. sin 70 cos 40 cos 70 sin 40In Problems 45-52, find the exact value of each expression. tan 8In Problems 45-52, find the exact value of each expression. sin 5 8In Problems 53-57, use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( ) (d) tan( + ) (e) sin( 2 ) (f) cos( 2 ) (g) sin 2 (h) sin( + ) sin= 4 5 ,0 2 ;sin= 5 13 , 2In Problems 53-57, use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( ) (d) tan( + ) (e) sin( 2 ) (f) cos( 2 ) (g) sin 2 (h) sin( + ) sin= 3 5 , 3 2 ;cos= 12 13 , 3 2 2In Problems 53-57, use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( ) (d) tan( + ) (e) sin( 2 ) (f) cos( 2 ) (g) sin 2 (h) sin( + ) tan= 3 4 , 3 2 ;tan= 12 5 ,0 2In Problems 53-57, use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( ) (d) tan( + ) (e) sin( 2 ) (f) cos( 2 ) (g) sin 2 (h) sin( + ) sec=2, 2 0;sec=3, 3 2 2In Problems 53-57, use the information given about the angles and to find the exact value of: (a) sin( + ) (b) cos( + ) (c) sin( ) (d) tan( + ) (e) sin( 2 ) (f) cos( 2 ) (g) sin 2 (h) sin( + ) sin= 2 3 , 3 2 ;cos= 2 3 , 3 2In Problems 58-63, find the exact value of each expression. cos( sin 1 3 5 cos 1 1 2 )In Problems 58-63, find the exact value of each expression. sin( cos 1 5 13 cos 1 4 5 )In Problems 58-63, find the exact value of each expression. tan( sin 1 ( 1 2 ) tan 1 3 4 )In Problems 58-63, find the exact value of each expression. cos( tan 1 ( 1 )+ cos 1 ( 4 5 ) )In Problems 58-63, find the exact value of each expression. sin[ 2 cos 1 ( 3 5 ) ]In Problems 58-63, find the exact value of each expression. cos( 2 tan 1 4 3 )In Problems 64-75, solve each equation on the interval 02 . cos= 1 2In Problems 64-75, solve each equation on the interval 02 . tan+ 3 =0In Problems 64-75, solve each equation on the interval 02 . sin( 2 )+1=0In Problems 64-75, solve each equation on the interval 02 . tan( 2 )=0In Problems 64-75, solve each equation on the interval 02 . sec 2 =4In Problems 64-75, solve each equation on the interval 02 . 0.2sin=0.05In Problems 64-75, solve each equation on the interval 02 . sin+sin( 2 )=0In Problems 64-75, solve each equation on the interval 02 . sin( 2 )cos2sin+1=0In Problems 64-75, solve each equation on the interval 02 . 2 sin 2 3sin+1=0In Problems 64-75, solve each equation on the interval 02 . 4 sin 2 =1+4cosIn Problems 64-75, solve each equation on the interval 02 . sin( 2 )= 2 cosIn Problems 64-75, solve each equation on the interval 02 . sincos=1In Problems 76 - 80, use a calculator to find an approximate value for each expression, rounded to two decimal places. sin 1 0.7In Problems 76 - 80, use a calculator to find an approximate value for each expression, rounded to two decimal places. tan 1 ( 2 )In Problems 76 - 80, use a calculator to find an approximate value for each expression, rounded to two decimal places. cos 1 ( 0.2 )79RE80REIn Problems 81-83, use a graphing utility to solve each equation on the interval 0x2 Approximate any solutions rounded to two decimal places. 2x=5cosxIn Problems 81-83, use a graphing utility to solve each equation on the interval 0x2 Approximate any solutions rounded to two decimal places. 2sinx+3cosx=4xIn Problems 81-83, use a graphing utility to solve each equation on the interval 0x2 Approximate any solutions rounded to two decimal places. sinx=lnxIn Problems 84 and 85, find the exact solution of each equation. 3 sin 1 x=In Problems 84 and 85, find the exact solution of each equation. 2 cos 1 x+=4 cos 1 xUse a Half-angle Formula to find the exact value of sin 15 . Then use a difference formula to find the exact value of sin 15 Show that the answers found are the same.If you are given the value of cos and want the exact value of cos( 2 ) , what form of the Double-angle Formula for cos( 2 ) is most efficient to use?1CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CT19CT20CT21CT22CT23CT24CT25CT26CT27CT28CT29CT1CR2CR3CR4CR5CR6CR7CR8CR9CR