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All Textbook Solutions for Trigonometry (MindTap Course List)

55PS 56PS 57PS 58PS Prove each identity. cotcsc=cos 2CT Prove each identity. seccos=tansin 4CT 5CT 6CT 7CT 8CT 9CT 10CT 11CT 12CT Let sinA=35 with 270A360 and cosB=817 with 90B180 and find the following. sin(A+B)Let sinA=35 with 270A360 and cosB=817 with 90B180 and find the following. cos(AB)15CT Let sinA=35 with 270A360 and cosB=817 with 90B180 and find the following. sinA2 17CT 18CT 19CT 20CT 21CT 22CT 23CT 24CT 25CT 26CT 27CT 28CT 29CT 30CT 1GP 2GP 3GP 4GP 5GP 1RP 1PS 2PS 3PS 4PS 5PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. cos=1 For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. sin=32 For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. cos=22 9PS 10PS For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Use a calculator to approximate to all answers to the nearest hundredth. sinx=0.25 12PS For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Use a calculator to approximate to all answers to the nearest hundredth. cosx=0.1250 14PS For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Use a calculator to approximate to all answers to the nearest hundredth. tanx=2.5 For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Use a calculator to approximate to all answers to the nearest hundredth. tanx=0.25 For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. 2sin=1 18PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. 2cos3=0 20PS 21PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Don not use a calculator. 2tan+2=0 23PS 24PS 25PS For each of the following equations, solve for (a) all radian solutions and (b) t if 0t2. Give all answers as exact values in radians. Do not use a calculator. 5cost+23=cost For each of the following equations, solve for (a) all radian solutions and (b) t if 0t2. Give all answers as exact values in radians. Do not use a calculator. 3sint+5=2sint 28PS 29PS 30PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Approximate all answers to the nearest tenth of a degree. 2cos5=3cos2 32PS 33PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Approximate all answers to the nearest tenth of a degree. sin4=2sin 35PS 36PS 37PS 38PS 39PS 40PS 41PS 42PS For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Give all answers as exact values in radians. Do not use a calculator. 2sin2xsinx1=0 For each of the following equations, solve for (a) all radian solutions and (b) x if 0x2. Give all answers as exact values in radians. Do not use a calculator. 2cos2x+cosx1=0 45PS 46PS 47PS 48PS 49PS 50PS 51PS For each of the following equations, solve for (a) all degree solutions and (b) if 0360. Do not use a calculator. 2cos2+2cos1=0 53PS 54PS 55PS 56PS 57PS 58PS 59PS 60PS 61PS 62PS 63PS 64PS 65PS 66PS 67PS 68PS 69PS 70PS 71PS 72PS 73PS 74PS 75PS 76PS 77PS 78PS 79PS 80PS 81PS 82PS 83PS 84PS 85PS 86PS 87PS 88PS Motion of a Projectile If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation (see Figure 10), then the height h of the projectile at time t is given by h=16t2+vtsin Give the equation for the height, if v is 1,500 feet per second and is 30.Motion of a Projectile If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation (see Figure 10), then the height h of the projectile at time t is given by h=16t2+vtsin Give the equation for h, if v is 600 feet per second and is 45. (Leave your answer in exact value form.)91PS 92PS Find the angle of elevation of a rifle barrel, if a bullet fired at 1,500 feet per second takes 2 seconds to reach a height of 750 feet. Give your answer to the nearest tenth of a degree.94PS Write cos2A in terms of sinA only.Write cos2A in terms of cosA only.97PS 98PS 99PS 100PS 101PS Prove the identity sin2x=2tanx+cotx.103PS In solving cosx+2sinxcosx=0, which of the following is the best first step? Write 2sinxcosx as sin2x. Factor cosx from the left side. Divide both sides by cosx. Subtract cosx from both sides.105PS 106PS For Question 1 through 4, fill in the blank with an appropriate word. To solve an equation containing secant, cosecant, or cotangent functions, first rewrite each function using a identity and then fractions by both sides of the equation by the least common denominator.2PS For Question 1 through 4, fill in the blank with an appropriate word. When solving an equation containing a single sine and cosine, sometimes it is necessary to both sides of the equation so that the Pythagorean identity can be used. Just be sure to check for solutions.4PS 5PS Solve each equation for if 0360. 2csc=2 7PS 8PS 9PS 10PS Solve each equation for if 0360. sec2tan=0 Solve each equation for if 0360. csc+2cot=0 13PS 14PS 15PS Solve each equation for if 0360. 2cos+1=sec 17PS 18PS 19PS 20PS Solve each equation for x if 0x2. Give your answers in radians using exact values only. 2cos2x+sinx1=0 22PS 23PS Solve each equation for x if 0x2. Give your answers in radians using exact values only. 4cos2x4sinx5=0 25PS 26PS 27PS Solve each equation for x if 0x2. Give your answers in radians using exact values only. sinxcosx=2 29PS 30PS 31PS 32PS 33PS Solve for if 0360. sin2+cos=1 35PS 36PS 37PS 38PS 39PS 40PS 41PS 42PS 43PS 44PS 45PS 46PS 47PS 48PS 49PS 50PS Solving the following equations will require you to use the quadratic formula. Solve each equation for between 0 and 360, and round your answers to the nearest tenth of a degree. 2sin22cos1=0 52PS 53PS 54PS 55PS 56PS 57PS 58PS 59PS 60PS 61PS 62PS 63PS 64PS 65PS 66PS 67PS 68PS 69PS 70PS 71PS 72PS 73PS 74PS For Question 1 through 3, fill in the blank with an appropriate word or expression. To solve a trigonometric equation involving a multiple angle n, first find the possible values of, then divide by to find the values of .For Question 1 through 3, fill in the blank with an appropriate word or expression. For a trigonometric equation involving cosn in degrees, add to the values of to find all coterminal solutions If solving in radians, add to the values of to find all coterminal solutions.3PS 4PS 5PS 6PS 7PS 8PS 9PS 10PS Find all solutions if 0x2. Use exact values only. Verify your answer graphically. cos2x=22 12PS 13PS 14PS Find all solutions if 0x2. Use exact values only. Verify your answer graphically. tan2x=3 16PS 17PS Find all degree solutions for each of the following: cos2=22 19PS 20PS 21PS 22PS 23PS Use your graphing calculator to find all degree solutions in the interval 0x360 for each of the following equations. cos2x=12 25PS 26PS 27PS Use your graphing calculator to find all degree solutions in the interval 0x360 for each of the following equations. tan2x=1 29PS Find all solutions in radians. Approximate your answers to the nearest hundredth. sin(3x+5)=0.4 31PS 32PS 33PS 34PS 35PS 36PS 37PS 38PS 39PS Find all solutions in radians using exact values only. sin2xcos3x+cos2xsin3x=1 41PS 42PS Find all solutions in radians using exact values only. cos35x=1 44PS 45PS 46PS 47PS 48PS 49PS 50PS Find all solutions in radians. Approximate your answers to the nearest hundredth. 159cos(6t5)=11 Find all solutions in radians. Approximate your answers to the nearest hundredth. 7+12sin(5t+3)=2 53PS 54PS 55PS 56PS 57PS Find all solutions if 0360. When necessary, round your answers to the nearest tenth of a degree. cossin=1 59PS 60PS 61PS 62PS 63PS 64PS Ferris Wheel In example 6 of Section 4.5, we found the equation that gives the height h of a passenger on a Ferris wheel at any time t during the ride to be h=139125cos10t where h is given in feet and t is given in minutes. Use this equation to find the times at which a passenger will be 100 feet above the ground. Round your answer to the nearest tenth of a minute. Use your graphic calculator to graph the function and verify your answers.Ferris Wheel In Problem 37 of Problem Set 4.5, you found the equation that gives the height h of a passenger on a Ferris wheel at any time t during the ride to be h=110.598.5cos215t where the units for h are feet and the units for t are minutes. Use this equation to find the times at which a passenger will be 100 feet above the ground. Round your answers to the nearest tenth of a minute. Use your graphing calculator to graph the function and verify your answers.Geometry The following formula gives the relationship the number of sides n, the radius r, and the length of each side I in a regular polygon (Figure 8). Find n, if l=r.Geometry If central angle cuts off a chord of length c in a circle of radius r (Figure 9), then the relationship , c, and r is given by 2rsin2=c Find ,c=3r.69PS 70PS Alternating Current The voltage of the alternating current through an electrical outlet can be modeled by the function V(t)=163sin(120t), where t is in seconds and V in volts Find all times at which the voltage is at its maximum.72PS Oscillating Spring A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function d(t)=3.5cos(2t), where d is measured in centimeters (Figure 12). Find all times at which the displacement is zero.74PS 75PS 76PS 77PS 78PS 79PS 80PS

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