MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express answer as a multiple of. 1) 6 1) radians 6 radians C) radians 7 radians ) -60 ) - radians - radians C) - radians - radians ) 1 ) 1 radians radians C) radians radians ) - 16 ) - radians radians C) - radians radians Convert the angle in radians to degrees. ) 11 ) C) 9 6 6) - 6) C) ) 7) 900 C) 0 Draw the angle in standard position. ) - ) 9) 7 9) 10) ) 1

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a positive angle less than 60 or that is coterminal with the given angle. 11) -7 11) 17 C) 7 1) 16 1) 6 11 C) ) 1) 17 C) Use the Pythagorean Theorem to find the length of the missing side.then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. 1) Find sin. 1) C) ) Find csc. 1) 1 1 C) ) Find cos. 16) C)

3 17) Find tan. 9 17) C) 9 9 Find a cofunction with the same value as the given expression. 1) sin 1) cos cot 7 C) cos 7 tan 7 19) cos 69 19) sin 1 sec 69 C) sin 69 csc 1 0) tan 0) cot 11 cot C) cot 6 sec 1) csc 1) sec sec 11 C) sin sec 66 A point on the terminal side of angle is given. Find the exact value of each of the six trigonometric functions of, or state that the function is undefined. ) (, -) ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let be an angle in standard position. Name the quadrant in which the angle lies. ) csc > 0, sec > 0 ) quadrant I quadrant IV C) quadrant II quadrant III Find the exact value of the each of the remaining trigonometric functions of. ) cot = - 9, cos < 0 ) ) sin = -, tan > 0 ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the amplitude or period as requested. 6) Period of y = cos 1 x 6) C)

4 7) Period of y = sin 6 x 7) 1 C) 6 Determine the phase shift of the function. ) y = 1 sin (x + ) ) units to the left C) - units to the left units to the left units to the right 9) y = sin x - 9) units up C) units down units to the left units to the right Graph the function. 0) y = sin x 0) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) y = sin x + 1)

5 C) Determine the amplitude or period as requested. ) Period of y = cos - 7 x ) 7 C) 16 7 Determine the phase shift of the function. ) y = cos x + ) units up units to the left C) units down units to the right

6 Graph the function. ) y = - 1 cos x ) C) 6

7 Use a vertical shift to graph the function. ) y = sin 1 x - ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 6) y = cos x - + 6) 7

8 C) Determine the phase shift of the function. 7) y = cos ( x - ) 7) units to the left units to the left C) units to the right units to the right Complete the identity. ) (sin x + cos x) 1 + sin x cos x =? ) sin x C) - sec x 0 9) sin x + sin x cot x =? 9) cot x C) sin x + 1 cot x - 1 0) cos x + sin x cos x - sin x - cos x sin x =? 0) 1 - sec x csc x sec x csc x C) + sec x csc x - sec x csc x Simplify the given expression: 1) (sec x + 1)(sec x - 1) =? 1) tan x ) tan x + cos x + sin x =? ) ) 1 - cos x 1 + sin x =? )

9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) 1 - cos x sin x =? ) -csc x - cot x csc x - cot x C) csc x + cot x csc x - cot x + 1 ) sec x csc x =? ) sec x + csc x sec x - csc x C) csc x - sec x sec x + csc x Verify the identity. 6) cscu - cos u sec u= cot u 6) 7) (1 + tanu)(1 - sinu) = 1 7) ) csc u - sin u = cos u cot u ) 9) 1 + secx sinx = secx 9) 0) cot x + csc x = csc x - 1 0) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) cos (17 ) cos ( ) + sin (17 ) sin ( ) 1) - - C) - 1-9

10 Complete the identity. ) cos x - 6 =? ) - C) (cos x + sin x) 1 (- cos x + sin x) (cos x - sin x) - (cos x - sin x) Use the given information to find the exact value of the expression. ) sin =, lies in quadrant II, and cos =, lies in quadrant I Find cos ( - ). ) C) Find the exact value by using a sum or difference identity. ) sin (1-9 ) ) C) - 1 ) sin 16 ) - ( - 1) ( - 1) C) - ( + 1) ( + 1) Find the exact value of the expression. 6) cos cos - sin sin 6) 1 C) 1 7) cos 9 sin 1 - cos 1 sin 9 7) 1 C) 1 1 Use the given information to find the exact value of the expression. ) sin =, lies in quadrant I, and cos =, lies in quadrant I Find cos ( + ). ) C) ) sin = 1 1, lies in quadrant II, and cos =, lies in quadrant I Find sin ( - ). 9) C)

11 60) tan = 0, lies in quadrant III, and cos = -, lies in quadrant II Find sin ( + ). 60) C) ) sin = 7, lies in quadrant II, and cos =, lies in quadrant I Find cos ( - ). 61) C) Find the exact value by using a difference identity. 6) tan 6) C) Use trigonometric identities to find the exact value. tan 0 + tan 110 6) 1 - tan 0 tan C) ) Find the exact value under the given conditions. 6) tan = 1, < < 1 ; cos = - 9, < < Find tan ( + ). 6) C) ) cos = - 7, < < ; sin = - 1, < < C) Find tan ( + ). 6) Use the figure to find the exact value of the trigonometric function. 66) Find sin. 66) C)

12 67) Find tan. 67) C) Use the given information to find the exact value of the expression. 6) sin =, lies in quadrant I Find cos. 6) C) 7 69) cos = 1, lies in quadrant IV Find sin. 69) C) ) tan = 1, lies in quadrant III Find sin. 70) C) Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 71) cos 1 - sin 1 71) - 1 C) 1 - tan 7) 7) 1 - tan 1 C) -1 Use a half-angle formula to find the exact value of the expression. 7) sin 16 7) C)

13 7) cos 1 7) C) Use the given information to find the exact value of the trigonometric function. 7) sin = 1, tan > 0 Find cos. 7) C) ) cos = -, sin > 0 Find cos. 76) 0 10 C) ) csc = -, tan > 0 Find cos. 77) C) Find all solutions of the equation. 7) sin x - = 0 7) x = + n or x = + n x = 6 + n or x = + n C) x = 6 + n or x = + n x = + n or x = + n 79) tan x sec x = - tan x 79) x = + n or x = + n or x = n x = + n or x = + n or x = n C) x = + n or x = + n or x = n x = + n or x = + n or x = n Solve the equation on the interval [0, ). 0) sin x = 0) 0 0,, C), 1, 6,, 7 1, 7 6, 1 1,, ) cos x + cos x + 1 = 0 1), 7 C), 1

14 ) sin x = sin x ) 6, 6, C) 0,, 6, 6,,, ) cos x = sin x ), 7, C), 7, Solve the equation on the interval [0, ). ) cot x cos x = cot x ) 0,, C) 0,, Solve the equation on the interval [0, ). ) sec x - = tan x ) 6 no solution C) 6) cos x = 6) 0,,, C), 7, 9, 1,,, 7 no solution 7) sin x = 1 7) 0,,,,,, 7 C), 9 no solution ) cos x = - cos x ) 0,,, C), 7, 9, 1,,, 7 no solution 9) sin x + sin x = 0 9), 9 0,,, C),,, 7 no solution Use a calculator to solve the equation on the interval [0, ). Round the answer to two decimal places. 90) cos x = ) 0.7,.1 0.7,. C) 0.7,. 0.7,.0 91) sin x = ) 0.9,. 0.9,.99 C) 0.9, ,. 1

15 Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) B = 6 C = 107 b = 1 A =, a = 1., c = 19.6 A = 7, a = 19.6, c = 1. C) A =, a =., c = 1.6 A = 7, a = 1.6, c =. 9) Two sides and an angle (SS of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) A = 0, a = 7, b = 1 9) B = 60, C = 60, c = 1.1 no triangle C) B = 90, C = 60, c = 1.1 B = 60, C = 90, c = 1.1 9) B =, b = 1, a = 9) A = 1, C = 11, c = A =, C = 116, c =. C) no triangle A = 9, C = 117, c = 0 9) B =, b =.9, a =. 9) A1 = 0, C1 = 1, c1 =.9; A = 10, C =, c = 0. A = 10, C =, c = 0. C) A = 0, C = 1, c =.9 no triangle Find the area of the triangle having the given measurements. Round to the nearest square unit. 96) B = 1, a = feet, c = 9 feet 96) 17 square feet square feet C) 9 square feet 19 square feet Solve the problem. 97) A surveyor standing 9 meters from the base of a building measures the angle to the top of the building and finds it to be. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 6. How tall is the radio tower? 11.7 meters 19.7 meters C) 7. meters.6 meters 97) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) a = 7, b = 1, c = 1 9) A =, B = 70, C = A = 6, B = 70, C = C) A = 0, B = 6, C = no triangle 99) b = 6, c = 10, A = ) a = 1.9, B =, C = 9 a = 1.1, B = 6, C = 7 C) a = 16, B =, C = no triangle Solve the problem. 100) Two airplanes leave an airport at the same time, one going northwest (bearing 1 ) at mph and the other going east at 7 mph. How far apart are the planes after hours (to the nearest mile)? 70 miles 10 miles C) 117 miles 16 miles 100) 1