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All Textbook Solutions for Trigonometry (MindTap Course List)

90E Solving for In Exercises 91-96, find two solutions of each equation. Give your answers in degrees 0360 and in radians 02. Do not use a calculator. asin=12bsin=12 92E 93E 94E 95E 96E 97E 98E 99E Sales A company that produces snowboards forecasts monthly sales over the next 2 years to be S=23.1+0.442t+4.3cost6 where S is measured in thousands of units and t is the time in months, with t=1 corresponding to January 2017. Predict the sales for each of the following months. a February 2017 b February 2018 c June 2017 d June 2018 101E 102E 103E 104E 105E 106E Sketch the graph of y=2cosx on the interval 2,92.2ECP 3ECP 4ECP 5ECP 6ECP 7ECP 1E 2E 3E 4E Finding the Period and Amplitude In Exercises 5-12, find the period and amplitude. y=2sin5x Finding the Period and Amplitude In Exercises 5-12, find the period and amplitude. y=3cos2x Finding the Period and Amplitude In Exercises 5-12, find the period and amplitude. y=34cosx2 8E Finding the Period and Amplitude In Exercises 5-12, find the period and amplitude. y=12sin5x4 10E 11E Finding the Period and Amplitude In Exercises 5-12, find the period and amplitude. y=25cos10x Describing the Relationship Between Graphs In Exercises 13-24, describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts. fx=cosx gx=cos5x 14E Describing the Relationship Between Graphs In Exercises 13-24, describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts. fx=cos2x gx=cos2x 16E 17E 18E 19E 20E Describing the Relationship Between Graphs In Exercises 13-24, describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.Describing the Relationship Between Graphs In Exercises 13-24, describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts.23E 24E 25E 26E 27E 28E 29E 30E 31E Sketching the Graph of a Sine or Cosine Function In Exercises 31-52, sketch the graph of the function. (Include two full periods.) y=14sinx 33E 34E 35E 36E 37E 38E 39E Sketching the Graph of a Sine or Cosine Function In Exercises 31-52, sketch the graph of the function. (Include two full periods.) y=10cosx6 41E 42E 43E Sketching the Graph of a Sine or Cosine Function In Exercises 31-52, sketch the graph of the function. (Include two full periods.) y=4cosx+4 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E 64E Graphical Reasoning In Exercises 65-68, find a and d for the function fx=acosx+d such that the graph of f matches the figure.Graphical Reasoning In Exercises 65-68, find a and d for the function fx=acosx+d such that the graph of f matches the figure.67E Graphical Reasoning In Exercises 65-68, find a and d for the function fx=acosx+d such that the graph of f matches the figure.Graphical Reasoning In Exercises 69-72, find a,b, and c for the function f(x)=asin(bxc) such that the graph of f matches the figure.Graphical Reasoning In Exercises 69-72, find a,b, and c for the function f(x)=asin(bxc) such that the graph of f matches the figure.71E 72E 73E 74E 75E 76E 77E 78E 79E For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is modeled by v=0.85sint/3, where t is the time (in seconds). a Find the time for one full respiratory cycle. b Find the number of cycles per minute. c Sketch the graph of the velocity function. Use the graph to confirm your answer in part a by finding two times when new breaths begin. (Inhalation occurs when v0, and exhalation occurs when v0.)81E Piano Tuning When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by y=0.001sin880t, where t is the time (in seconds). a What is the period of the function? b The frequency f is given by f=1/p. What is the frequency of the note?Astronomy The table shows the percent y (in decimal form) of the moon’s face illuminated on day x in the year 2018, where x=1 corresponds to January 1. (a) Create a scatter plot of the data. (b) Find a trigonometric model for the data. (c) Add the graph of your model in part (b) to the scatter plot. How well does the model fit the data? (d) What is the period of the model? (e) Estimate the percent of the moon’s face illuminated on March 12,2018.Meteorology The table shows the maximum daily high temperatures (in degrees Fahrenheit) in LasVegas. and International Falls I for month t, where t=1 corresponds to January. (a) A model for the temperatures in LasVegas is Lt=80.60+23.50cost63.67.L Find a trigonometric model for the temperatures in International Falls. (b) Use a graphing utility to graph the data points and the model for the temperatures in LasVegas. How well does the model fit the data? (c) Use the graphing utility to graph the data points and the model for the temperatures in International Falls. How well does the model fit the data? (d) Use the models to estimate the average maximum temperature in each city. Which value in each model did you use? Explain. (e) What is the period of each model? Are the periods what you expected? Explain. (f) Which city has the greater variability in temperature throughout the year? Which value in each model determines this variability? Explain.Ferris Wheel The height h (in feet) above ground of a seat on a Ferris wheel at time t (in seconds) is modeled by ht=53+50sin10t2. (a) Find the period of the model. What does the period tell you about the ride? (b) Find the amplitude of the model. What does the amplitude tell you about the ride? (c) Use a graphing utility to graph one cycle of the model.Fuel Consumption The daily consumption C (in gallons) of diesel fuel on a farm is modeled by C=30.3+21.6sin2t365+10.9 where t is the time (in days), with t=1 corresponding to January 1. (a) What is the period of the model? Is it what you expected? Explain. (b) What is the average daily fuel consumption? Which value in the model did you use? Explain. (c) Use a graphing utility to graph the model. Use the graph to approximate the time of the year when consumption exceeds 40 gallons per day.87E True or False? In Exercises 87-89, determine whether the statement is true or false. Justify your answer. The function y=12cos2x has an amplitude that is twice that of the function y=cosx.True or False? In Exercises 87-89, determine whether the statement is true or false. Justify your answer. The graph of y=cosx is a reflection of the graph of y=sinx+/2 in the xaxis.90E 91E 92E 93E 94E 95E 1ECP 2ECP 3ECP 4ECP 5ECP 6ECP 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E Solving a Trigonometric Equation In Exercises 49-56, find the solutions of the equation in the interval 2,2. Use a graphing utility to verify your results. secx=2 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E 81E 82E Meteorology The normal monthly high temperatures H (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by Ht=57.5418.53cost614.03sint6 and the normal monthly low temperatures L are approximated by Lt=42.0315.99cost614.32sint6 where t is the time (in months), with t=1 corresponding to January (see figure). (a) What is the period of each function ? (b) During what part of the year is the difference between the normal high and normal low temperatures greatest ? When is it least ? (c) The sun is northernmost in the sky around June 21, but the graph shows the warmest temperatures at a later date. Approximate the lag time of the temperatures relative to the position of the sun.Sales The projected monthly sales S (in thousands of units) of lawn mowers are modeled by S=74+3t40cost6 where t is the time (in months), with t=1 corresponding to January. (a) Graph the sales function over 1 year. (b) What are the projected sales for June ?85E Distance A plane flying at an altitude of 7 miles above a radar antenna passes directly over the radar antenna (see figure). Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. ( d is positive as the plane approaches the antenna.) Write d as a function of x and graph the function over the interval 0x.87E 88E 89E 90E 91E 92E 93E 94E If possible, find the exact value of each expression a. arcsin1 b. sin12 2ECP 3ECP Use a calculator to approximate the value of each expression, if possible. a. arctan4.84 b. arcsin1.1 c. arccos0.349 5ECP 6ECP 7ECP 1E 2E Fill in the blanks. FunctionAlternativeNotationDomainRange y =arctanx 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E Finding Missing Coordinates In Exercises 37 and 38, determine the missing coordinates of the points on the graph of the function.39E 40E 41E 42E 43E Using an Inverse Trigonometric Function In Exercises 39-44, use an inverse trigonometric function to write as a function of x.Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. sinarcsin0.3 Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. tanarctan45 Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. cosarccos3 Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. sinarcsin0.2 Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. arcsinsin9/4 Using Inverse Properties In Exercises 45-50, find the exact value of the expression, if possible. arccoscos3/2 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. sinarctan34 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. cosarcsin45 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. costan12 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. sincos15 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. secarcsin513 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. cscarctan512 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. cotarctan35 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. secarccos34 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. tanarccos23 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. cotarctan58 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. csccos132 Evaluating a Composition of Functions In Exercises 51-62, find the exact value of the expression, if possible. tansin122 63E 64E 65E 66E 67E 68E 69E 70E Writing an Expression In Exercises 63-72, write an algebraic expression that is equivalent to the given expression. cscarctanxa 72E 73E 74E

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