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All Textbook Solutions for Precalculus

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What is the distance between these points? What is their midpoint?3CR Use the transformations to graph the equation y=|x3|+2.5CR 6CR 7CR 8CR 9CR 10CR Consider the function f(x)=2x5x44x3+2x2+2x1 Find the real zeros and their multiplicity. Find the intercepts. Find the power function that the graph of f resembles for large x. Graph f using a graphing utility. Approximate the turning points, if any exist. Use the information obtained in parts (a)(e) to graph f by hand. Identify the intervals on which f is increasing, decreasing, or constant.12CR 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU y= sin 1 x means _____, where 1x1 and 2 y 2 .8AYU 9AYU 10AYU 11AYU 12AYU In Problems 15-26, find, the exact value sin 1 0 In Problems 15-26, find, the exact value of each expression. cos 1 1 In Problems 15-26, find, the exact value of each expression. sin 1 ( 1 )In Problems 15-26, find, the exact value of each expression. cos 1 ( 1 )In Problems 15-26, find, the exact value of each expression. tan 1 0 In Problems 15-26, find, the exact value of each expression. tan 1 ( 1 )In Problems 15-26, find, the exact value of each expression. sin 1 2 2 In Problems 15-26, find, the exact value of each expression. tan 1 3 3 In Problems 15-26, find, the exact value of each expression. tan 1 3 In Problems 15-26, find, the exact value of each expression. sin 1 ( 3 2 )In Problems 15-26, find, the exact value of each expression. cos 1 ( 3 2 )In Problems 15-26, find, the exact value of each expression. sin 1 ( 2 2 )In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. sin 1 0.1 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. cos 1 0.6 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. tan 1 5 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. tan 1 0.2 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. cos 1 7 8 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. sin 1 1 8 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. tan 1 ( 0.4 )In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. tan 1 ( 3 )In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. sin 1 ( 0.12 )In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. cos 1 ( 0.44 )In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. cos 1 2 3 In Problems 27-38, use a calculator to find the value of each expression rounded to two decimal places. sin 1 3 5 In Problems 39-62, 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( 3 8 ) ]In Problems 39-62, 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 4 5 )In Problems 39-62, 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( 3 8 ) ]In Problems 39-62, 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 7 ) ]In Problems 39-62, 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 9 8 )In Problems 39-62, 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( 5 3 ) ]In Problems 39-62, 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 4 5 )In Problems 39-62, 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 ) ]In Problems 39-62, 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 1 4 )In Problems 39-62, 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 ( 2 3 ) ]In Problems 39-62, 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 4 )In Problems 39-62, 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 ( 2 ) ]In Problems 39-62, 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 1.2 )In Problems 39-62, 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 ( 2 ) ]In Problems 39-62, 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 )In Problems 39-62, 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 ( 1.5 ) ]In Problems 63-70, 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 )=5sinx+2; 2 x 2 In Problems 63-70, 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 )=2tanx3; 2 x 2 In Problems 63-70, 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 )=2cos( 3x );0x 3 In Problems 63-70, 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 )=3sin( 2x ); 4 x 4 In Problems 63-70, 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 )=tan( x+1 )3;1 2 x 2 1 In Problems 63-70, 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 )=cos( x+2 )+1;2x2 In Problems 63-70, 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 )=cos( x+2 )+1;2x2 In Problems 63-70, 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 )=2cos( 3x+2 ); 2 3 x 2 3 + 3 Find the exact solution of each equation. 4 sin 1 x=Find the exact solution of each equation. 2 cos 1 x=Find the exact solution of each equation. 3 cos 1 ( 2x )=2 Find the exact solution of each equation. 6 sin 1 ( 3x )=Find the exact solution of each equation. 3 tan 1 x=In Problems 71-78, find the exact solution of each equation. 4 tan 1 x=In Problems 71-78, find the exact solution of each equation. 4 cos 1 x2=2 cos 1 x In Problems 71-78, find the exact solution of each equation. 5 sin 1 x2=2 sin 1 x3 In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 (tanitan) must be expressed in radians. Approximate the number of hours of daylight in Houston, Texas ( 29 45 north latitude), for the following dates: (a) Summer solstice ( i= 23.5 ) (b) Vernal equinox ( i= 0 ) (c) July 4 ( i= 22 48 )In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle between the equatorial plane and ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 ( tanitan ) must be expressed in radians. Approximate the number of hours of daylight in New York, New York ( 4045 north latitude), for the following dates: Summer solstice (i=23.5) Vernal equinox ( i=0 ) July 4 ( i=2248 )In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 (tanitan) must be expressed in radians. Approximate the number of hours of daylight in Honolulu, Hawaii ( 21 18 north latitude), for the following dates: (a) Summer solstice ( i= 23.5 ) (b) Vernal equinox ( i= 0 ) (c) July 4 ( i= 22 48 )In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 (tanitan) must be expressed in radians. Approximate the number of hours of daylight in Anchorage, Alaska ( 61 10 north latitude), for the following dates: (a) Summer solstice ( i= 23.5 ) (b) Vernal equinox ( i= 0 ) (c) July 4 ( i= 22 48 )In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 (tanitan) must be expressed in radians. Approximate the number of hours of daylight at the Equator ( 0 north latitude) for the following dates: Summer solstice ( i= 23.5 ) Vernal equinox i= 0 July 4 i= 0 ( i= 22 48 ) What do you conclude about the number of hours of daylight throughout the year for a location at the Equator?In Problems 79-84, use the following discussion. The formula D=24[ 1 cos 1 ( tanitan ) ] can be used to approximate the number of hours of daylight D when the declination of the Sun is i at a location north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. See the figure. To use the formula, cos 1 (tanitan) must be expressed in radians. that is 66 30 north latitude for the following dates: (a) Summer solstice ( i= 23.5 ) (b) Vernal equinox ( i= 0 ) (c) July 4 ( i= 22 48 ) (d) Thanks to the symmetry of the orbital path of Earth around the Sun, the number of hours of daylight on the winter solstice may be found by computing the number of hours of daylight on the summer solstice and subtracting this result from 24 hours. Compute the number of hours of daylight for this location on the winter solstice. What do you conclude about daylight for a location at 66 30 north latitude?Being the First to See the Rising Sun Cadillac Mountain, elevation 1530 feet, is located in Acadia National Park. Maine, and is the highest peak on the east coast of the United States. It is said that a person standing on the summit will be the first person in the United States to see the rays of the rising Sun. How much sooner would a person atop Cadillac Mountain see the first rays than a person standing below, at sea level? [Hint: Consult the figure. When the person at D sees the first rays of the Sun, the person at F does not. The person at F sees the first rays of the Sun only after Earth has rotated so that F is at location Q . Compute the length of the arc subtended by the central angle . Then use the fact that at the latitude of Cadillac Mountain, in 24 hours a length of 2( 2710 )17,027.4 miles is subtended.]Movie Theater Screens Suppose that a movie theater has a screen that is 28 feet tall. When you sit down, the bottom of the screen is 6 feet above your eye level. The angle formed by drawing a line from your eye to the bottom of the screen and another line from your eye to the top of the screen is called the viewing angle. In the figure, is the viewing angle. Suppose that you sit x feet from the screen. The viewing angle is given by the function (x)= tan 1 ( 34 x ) tan 1 ( 6 x ) . What is your viewing angle if you sit 10 feet from the screen? 15 feel? 20 feel? If there are 5 feet between the screen and the first row of seats and there are 3 feet between each row and the row' behind it. which row results in the largest viewing angle? Using a graphing utility, graph ( x )= tan 1 ( 34 x ) tan 1 ( 6 x ) . What value of x results in the largest viewing angle?77AYU 78AYU 79AYU 80AYU What is the domain and the range of y=secx ?True or False The graph of y=secx is one-to-one on the interval [ 0, 2 ) and on the interval ( 2 , ] . (pp. 427-428)If tan= 1 2 , 2 2 , then sin= ______.y= sec 1 x means ________, where | x | ______ and ______ y ______, y 2 .y= sec 1 x means ________, where | x | ______ and ______ y ______, y 2 .True or False It is impossible to obtain exact values for the inverse secant function.True or False csc 1 0.5 is not defined.True or False The domain of the inverse cotangent function is the set of real numbers.9AYU 10AYU 11AYU 12AYU 13AYU 14AYU 15AYU 16AYU 17AYU 18AYU 19AYU 20AYU 21AYU 22AYU 23AYU 24AYU 25AYU 26AYU 27AYU 28AYU 29AYU 30AYU 31AYU 32AYU 33AYU 34AYU 35AYU 36AYU In Problems 37-44, find the exact value of each expression. cot 1 3 In Problems 37-44, find the exact value of each expression. cot 1 1 In Problems 37-44, find the exact value of each expression. csc 1 ( 1 )In Problems 37-44, find the exact value of each expression. csc 1 2 In Problems 37-44, find the exact value of each expression. sec 1 2 3 3 In Problems 37-44, find the exact value of each expression. sec 1 ( 2 )In Problems 37-44, find the exact value of each expression. cot 1 ( 3 3 )In Problems 37-44, find the exact value of each expression. csc 1 ( 2 3 3 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. sec 1 4 In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. csc 1 5 In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. cot 1 2 In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. sec 1 ( 3 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. csc 1 ( 3 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. cot 1 ( 1 2 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. cot 1 ( 5 )52AYU In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. csc 1 ( 3 2 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. sec 1 ( 4 3 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. cot 1 ( 3 2 )In Problems 45-56, use a calculator to find the value of each expression rounded to two decimal places. cot 1 ( 10 )57AYU 58AYU 59AYU 60AYU 61AYU 62AYU 63AYU 64AYU 65AYU 66AYU 67AYU 68AYU 69AYU 70AYU 71AYU 72AYU 73AYU 74AYU 75AYU 76AYU 77AYU 78AYU Problems 79 and 80 require the following discussion: When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose is related to the height h and base radius r of the conical pile by the equation = cot 1 r h . See the illustration. Angle of Repose: Deicing Salt Due to potential transportation issues (for example, frozen waterways) deicing salt used by highway departments in the Midwest must be ordered early and stored for future use. When deicing salt is stored in a pile 14 feet high, the diameter of the base of the pile is 45 feet. (a) Find the angle of repose for deicing salt. (b) What is the base diameter of a pile that is 17 feet high? (c) What is the height of a pile that has a base diameter of approximately 122 feet? Source: The Salt Storage Handbook, 2013 Problems 79 and 80 require the following discussion: When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose is related to the height h and base radius r of the conical pile by the equation = cot 1 r h . See the illustration. Angle of Repose: Bunker Sand The steepness of sand bunkers on a golf course is affected by the angle of repose of the sand (a larger angle of repose allows for steeper bunkers). A freestanding pile of loose sand from a United States Golf Association (USGA) bunker had a height of 4 feet and a base diameter of approximately 6.68 feet. (a) Find the angle of repose for USGA bunker sand. (b) What is the height of such a pile if the diameter of the base is 8 feet? (c) A 6-foot-high pile of loose Tour Grade 50/50 sand has a base diameter of approximately 8.44 feet. Which type of sand (USGA or Tour Grade 50/50) would be better suited for steep bunkers?

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