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
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the fundamental identities to simplify the expression. 1) cos - cos sin2 A) tan2 B) sin C) cos3 Use a sum or difference identity to find the exact value. 2) sin 15° cos 105° + cos 15° sin 105° 3 3 A) B) 2 2 D) sec2 2) C) 1 4 D) - 1 2 Use the fundamental identities to find the value of the trigonometric function. 8 3) Find sin if sec = - and tan < 0. 5 A) - 39 8 B) 39 8 C) - Use the fundamental identities to simplify the expression. 4) 1 - sin2 A) cot2 B) - cos2 5 8 3) D) 39 64 4) C) cos2 D) cos Use identities to find the indicated value for each angle measure. 5 Find sin(2 ). 5) cos = , sin < 0 13 A) 119 169 B) - 119 169 5) C) - 120 169 D) 120 169 Use the fundamental identities to simplify the expression. sec2 x - tan x 6) tan x A) tan2 x 6) B) csc x C) cot x D) tan x Perform the transformation. 7) Write sec x in terms of sin x. 7) A) ± 1 - sin 2 x B) 1 - sin2 x 1 - sin2 x D) C) ± 1) 1 ± sin x 1 - sin2 x 1 - sin2 x ± 1 - sin2 x sin x Use a sum or difference identity to find the exact value. 8) sin 10° cos 50° + cos 10° sin 50° 1 1 A) B) 2 6 9) 8) C) 3 2 D) 3 3 tan 20° + tan 10° 1 - tan 20° tan 10° A) 9) 1 2 B) 3 3 C) 2 Use the fundamental identities to find the value of the trigonometric function. 10) Find sin if cot = - 6 and cos < 0. 37 1 A) - 37 B) C) 37 6 11) Find cos A) - 5 12 if sin =- 5 and 13 B) D) 3 D) 37 6 10) 11) is in quadrant III. 12 5 C) - 13 5 Perform the indicated operations and simplify the result so there are no quotients. 12) tan2 - 3 sin tan sec A) 1 + cot B) sin tan C) sec csc Decide whether the expression is or is not an identity. 13) sin2 x + cos2x = 1 A) Identity D) - 12 13 D) -2 tan2 13) B) Not an identity Complete the sentence so the result is an identity. Let x be any real number. 14) sin x = ( )(cos x) A) cot x B) sec x C) tan x 12) D) csc x 14) Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. 15) tan2 csc2 15) 2 2 3 A) sin B) tan C) sec D) cos Use the fundamental identities to find the value of the trigonometric function. 11 and is in quadrant III. 16) Find sin if cos = 6 A) - 25 36 B) 5 6 C) - 2 5 6 16) D) - 3 12 Find the exact value of the expression using the provided information. 1 1 17) Find sin(s - t) given that cos s = , with s in quadrant I, and sin t = , with t in quadrant II. 3 4 A) -12 2 - 1 30 B) -12 30 - 1 2 C) -30 2 - 1 12 D) -2 30 - 1 12 Use the fundamental identities to simplify the expression. 1 + sec cos 18) cot2 A) tan2 18) B) csc2 D) sec2 C) 1 Use identities to fill in the blank with the appropriate trigonometric function name. 1 19) sec 30° = 60° A) csc B) cos C) sin 19) D) sec Using a sum or difference identity, write the following as an expression involving functions of x. 20) sin (x + 45°) A) -cos x C) D) 2 2 cos x sin x 2 2 Tell whether the statement is true or false. 17 = cos cos - sin sin 21) cos 72 9 8 9 8 21) A) True B) False Use an identity to write the expression as a single trigonometric function or as a single number. 1 + cos 84° 22) 1 - cos 84° B) cot 42° Use a sum or difference identity to find the exact value. 23) tan(- 15°) 3+4 A) - 3 + 2 B) 2 C) sin 42° D) tan 42° 3-2 3-4 2 22) 23) C) D) Use an identity to write the expression as a single trigonometric function or as a single number. 24) sin 22.5° cos 22.5° 2 3 2 A) B) C) 3 D) 4 3 2 25) 2 cos2 75° - 1 3 A) 2 20) B) sin x 2 2 cos x + sin x 2 2 A) cos 42° 17) 24) 25) 1 B) 2 1 C) 2 3 3 D) 2 26) cos2 4x - sin2 4x 1 A) sin 16x 2 26) B) cos 4x C) cos 8x Write the product as a sum or difference of trigonometric functions. 27) cos 35° sin 21° 1 1 A) (cos 56° - cos 14°) B) (sin 56° + sin 14°) 2 2 C) 1 (cos 56° + cos 14°) 2 D) B) -2 sin 32° sin(-12°) D) -2 cos 32° sin(-12°) Write the product as a sum or difference of trigonometric functions. 30) 2 sin 5x sin 13x A) cos 8x - cos 18x C) B) cos 18x + cos 8x 1 (cos 18x + cos 8x) 2 D) sin 18x + sin 8x 4 27) 1 (sin 56° - sin 14°) 2 Rewrite the following as a product of trigonometric functions. 28) sin 19° + sin 35° A) 2 sin 27° sin(-8°) B) 2 cos 27° sin(-8°) C) 2 sin 27° cos(-8°) D) 2 cos 27° cos(-8°) 29) cos 20° - cos 44° A) -2 cos 32° cos(-12°) C) -2 sin 32° cos(-12°) D) 2 sin 4x 28) 29) 30)