Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Ch 6/7/8 Exam Review 12) tan Convert the angle to a decimal in degrees. Round the answer to two decimal places. 1) 90°52'19'' < 0, sin <0 In the problem, sin and cos are given. Find the exact value of the indicated trigonometric function. 5 2 , cos = Find sec . 13) sin = 3 3 Convert the angle to D° M' S'' form. Round the answer to the nearest second. 2) 13.79° Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. 14) sec2 70° - tan2 70° If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. 3) r = 9.6 inches, = 315°, s = ? Convert the angle in degrees to radians. Express the answer as multiple of . 4) -60° Find the exact value of the indicated trigonometric function of . 3 in quadrant III Find cot . 15) csc = - , 2 Convert the angle in radians to degrees. 8 5) 5 Graph the sinusoidal function. 16) y = 4 sin (3x) If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If necessary, round the answer to two decimal places. 6) = 4 radians, A = 99 square meters, r = ? In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 5 39 ) Find tan t. 7) ( , 8 8 Graph the function. A point on the terminal side of an angle is given. Find the exact value of the indicated trigonometric function of . 8) (-2, -3) Find tan . 17) y = -3 tan Solve the problem. 9) What is the domain of the sine function? Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 10) tan 390° Name the quadrant in which the angle 11) cos < 0, csc < 0 lies. 1 1 x 4 Find the phase shift of the function. 18) y = 4 cos -2x - 28) csc-1 2 3 Solve the equation on the interval 0 29) 2 cos + 3 = 2 Graph the function. 19) y = csc x + 30) 4 sin2 5 <2 . -3=0 31) 2 cos(2 ) = 3 Solve the equation on the interval [0, 2 ). 32) Suppose f(x) = cos - 1. Solve f(x) = 0. Solve the equation on the interval 0 2 = 33) cos 2 2 2 34) cos2 35) 2 sin2 Find the exact value of the expression. 2 20) sin-1 2 36) tan 38) 3 cot2 Find the exact value of the expression. Do not use a calculator. 3 22) cos-1 cos 5 23) tan-1 tan - +1=0 - 3 sin + sec 37) sin2 21) tan-1 (-1) -2=0 =1 - cos2 + cos - 4 csc =0 =1 Establish the identity. 39) sin2 (- ) + cos2 (- ) = 1 40) (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos 2 x 8 41) (tan v + 1)2 + (tan v - 1)2 = 2 sec2 v Find the inverse function f-1 of the function f. 24) f(x) = 8 cos x + 2 42) Find the exact value of the expression. 3 25) sec sin-1 2 26) tan cos-1 - + 2 cos <2 . tan u - 1 1 - cot u = tan u + 1 1 + cot u 43) 1 - 1 2 44) 27) sec-1 2 2 cos2 u = - sin u 1 - sin u csc + cot tan + sin = csc cot 45) sin csc + sin + csc = sin Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function. 24 , 0< < Find cos(2 ). 58) sin = 25 2 sin 46) cos x csc x tan x = 1 47) cot 2 x 1 - sin x = csc x + 1 sin x 59) sec 48) sin3 x cos2 x = sin x (cos2 x - cos4 x) in quadrant II. The point - 12 52) 9 sin 18 - cos 18 sin 9 61) sec(2 )= Find cos ( - ). = 1 , 4 value of sin 63) cos in quadrant II, find the exact - 6 = in csc2 csc2 - 2 5 cos 2 2 Express the sum or difference as a product of sines and/or cosines. 64) cos(7 ) - cos(3 ) 3 65) sin(6 ) - sin(4 ) Establish the identity. 55) cos x + 1 , y , on the circle 3 Express the product as a sum containing only sines or cosines. 62) sin(9 ) cos(5 ) Find the exact value under the given conditions. 4 2 < < ; cos = , 0 < < 53) sin = , 5 2 5 2 54) If sin Find sin(2 ). Establish the identity. tan 160° - tan 40° 1 + tan 160° tan 40° Solve the problem. >0 x 2 + y2 = 1, also lies on the terminal side of an angle quadrant III. 60) f(2 ) 50) sin 165° 51) cos 6 11 , csc 11 Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, evaluate the given function. The point (x, 3), on the circle x 2 + y2 = 7, also lies on the terminal side of an angle Find the exact value of the expression. 49) cos =- 3 1 cos x - sin x 2 2 Find the value of the indicated trigonometric function of the angle in the figure. Give an exact answer with a rational denominator. 66) Find the exact value of the expression. 4 3 56) cos tan-1 - sin-1 3 5 Solve the equation on the interval 0 57) sin = - 2 - cos 9 <2 . Find sin . 3 5 67) 10 7 Find cot . Find the exact value of the expression. Do not use a calculator. 68) csc2 60° - tan2 30° Solve the right triangle using the information given. Round answers to two decimal places, if necessary. 69) a = 8, B = 25°; Find b, c, and A. 70) a = 3, c = 6; Find b, A, and B. Solve the problem. 71) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 90 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 40°. What is the distance between the piling and the pier to the nearest foot? 4 Answer Key Testname: CH 6 AND 7 AND 8 EXAM REVIEW 1) 90.87° 2) 13°47'24'' 3) 52.8 in. 4) - 3 5) 288° 6) 15.88 m 39 7) 5 8) 3 2 9) all real numbers 3 10) 3 11) III 12) IV 3 13) 2 14) 1 15) 5 2 16) 5 Answer Key Testname: CH 6 AND 7 AND 8 EXAM REVIEW 17) 18) 6 units to the left 19) 20) 4 21) 22) 4 3 5 23) - 8 x-2 24) f-1 (x) = cos-1 8 25) 2 26) - 3 27) 28) 3 6 6 Answer Key Testname: CH 6 AND 7 AND 8 EXAM REVIEW 29) 30) 31) 2 4 , 3 3 3 2 4 5 , , 3 3 3 , 11 13 23 , , 12 12 12 , 12 32) {0} 3 9 11 , , 33) 8 8 8 34) { } 35) , 6 36) {0} 1 6 37) 0, 2 4 , 3 3 38) , 6 5 6 39) sin2 (- ) + cos2 (- ) = (-sin )2 + (cos )2 = sin2 + cos2 = 1 sin x cos x cos 2 x = sin 2 x - cos 2 x = (1 - cos 2 x)- cos 2 x = 1 - 2 cos 2 x. 40) (sin x)(tan x cos x + cot x cos x) = sin x cos x sin x 41) (tan v + 1)2 + (tan v - 1)2 = tan2 v + 2 tan v + 1 + tan2 v - 2 tan v + 1 = 2(tan2 v + 1) = 2 sec2 v 1 1 - cot u -1 cot u cot u tan u - 1 1 - cot u = = = 42) tan u + 1 1 1 + cot u 1 + cot u +1 cot u cot u 43) 1 - cos2 u 1 - sin2 u (1 - sin u)(1 + sin u) =1=1= 1 - (1 + sin u) = - sin u 1 - sin u 1 - sin u 1 - sin u 44) csc + cot tan + sin 45) sin csc + sin + csc = = 1 sin sin cos sin 1 sin + = + sin + sin 1 + sin 46) cos x csc x tan x = (cos x) 47) cos sin 1 sinx = 1 + cos sin sin + sin cos sin + sin sin + sin sin sin cos = (sin = 1 + cos sin + sin ) · cos 1 = sin (1 + cos ) sin sin sin sin + sin = sin sin x = 1. cos x cot 2 x csc2 x - 1 (csc x + 1)(csc x - 1) 1 sin x 1 - sin x . = = = csc x - 1 = = csc x + 1 csc x + 1 csc x + 1 sin x sin x sin x 48) sin3 x cos2 x = sin x (1 - cos2 x) (cos2 x) = sin x (cos2 x - cos4 x). 2( 3 - 1) 49) 4 50) · 2( 3 - 1) 4 7 sin · cos sin = csc cot Answer Key Testname: CH 6 AND 7 AND 8 EXAM REVIEW 51) 1 2 52) - 3 -6 + 4 21 53) 25 54) 1+3 5 8 55) cos x + 56) = cos x cos 6 - sin x sin 6 = 3 1 cos x - sin x. 2 2 24 25 57) 4 58) 59) 6 527 625 -5 11 18 60) - 4 3 7 61) sec(2 ) = 1 1 = cos(2 ) 1 - 2 sin2 62) 1 [sin(14 ) + sin(4 )] 2 63) 1 [cos(2 ) + cos(3 )] 2 = 1 sin2 1 sin2 -2 = csc2 csc2 - 2 64) -2 sin(5 ) sin(2 ) 65) 2 sin cos(5 ) 9 106 66) sin = 106 67) cot = 7 10 68) 1 69) b = 3.73 c = 8.83 A = 65° 70) b = 5.2 A = 30° B = 60° 71) 76 ft 8