tm5 - MAC 1114 Module Test 5 Name MULTIPLE CHOICE Choose...

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Unformatted text preview: MAC 1114 Module Test 5 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the given trigonometric function in terms of the indicated function. 1) cot θ in terms of cos θ 2 A) ±cos θ 1 - cos θ 1 - cos2 θ C) ± B) ± 1 - cos2 θ cos θ D) 1 + cos2 θ cos θ 1 cos θ Use the fundamental identities to find the value of the trigonometric function. 2) Find sin θ if cot θ = - 5 and cos θ < 0. A) - 26 B) 26 26 C) 26 5 D) - 1 5 Complete the sentence so the result is an identity. Let x be any real number. 3) =1 sin x A) cot x 4) cos x = (cot x)( A) sin x B) sec x C) tan x D) csc x B) sec x C) tan x D) csc x ) Show that the equation is not an identity by listing the value(s) of the variable from among 0, π , π , and - π for 42 4 which the equation is false. 5) sin2θ = cos2θ A) - π 4 6) (sin θ + cos θ)2 = 1 A) π 2 7) sin θ + cos θ = 1 A) π and - π 4 4 8) (tan θ + 1)2 = sec2 θ A) π and 0 2 B) π and - π 4 4 C) 0 and π 2 D) π 2 B) - π 4 C) 0 and π 2 D) π and - π 4 4 B) 0 and π 2 C) - π 4 D) π 2 B) π , π , and 0 42 C) π , π , and - π 42 4 D) π and - π 4 4 1 Use the fundamental identities to simplify the expression. 9) 1 + sec θ cos θ cot2θ A) csc2θ B) tan2θ C) sec2θ D) 1 B) cot2 x C) csc2 x D) csc x Simplify the expression. 2 10) cos x + cos x sec x sin2 x A) sec2 x Decide whether the expression is or is not an identity. 11) tan t cot t = 1 A) Identity B) Not an identity Perform the indicated operations and simplify the result. 2 12) (sin θ + cos θ) 1 + 2 sin θ cos θ A) 1 D) - sec2θ C) 1 - sin θ B) 0 Identify the equation as either an identity or not. 13) tan2x = sec2x - sin2x - cos2x A) Not an identity B) Identity Find the exact value of the expression using the provided information. 14) Find cos(A - B) given that cos A = A) 37 - 6 74 111 B) - 37 , with A in quadrant I, and sin B = 37 37 74 C) 37 73 111 Use the cofunction identities to find an angle θ that makes the statement true. 15) sin (5θ + 12°) = cos (2θ - 5°) A) θ = 17° B) θ = 40° C) θ = 83° 7 7 16) sin (θ + 4°) = cos (θ + 6°) A) θ = 17° 7 B) θ = 83° 7 2 3 , with B in quadrant IV. D) 37 + 6 74 111 D) θ = 10° C) θ = 40° Write in terms of the cofunction of a complementary angle. 17) cot 142.453 ° A) tan 37.547 ° B) cot 37.547 ° 2 D) θ = 10° C) tan 52.453 ° D) tan (-52.453 °) Use the cofunction identities to find an angle θ that makes the statement true. 18) sin (3θ - 17°) = cos (θ + 43°) A) θ = 6° B) θ = 10° C) θ = 16° D) θ = 90° Find the exact value of the expression using the provided information. 19) Find cos(A - B) given that sin A = A) 186 + 18 15 B) 3 3 , with A in quadrant IV, and sin B = - 186 18 C) 55 18 C) 15 2( 15 6 5 , with B in quadrant IV. D) 55 + 18 15 2( 3 - 1) Use an appropriate identity to find the exact value of the expression. 20) cos 5π 12 A) - 3 + 1) 2( 4 B) 3 - 1) 2( 4 3 3 + 1) 4 D) - 4 ...
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This note was uploaded on 10/18/2011 for the course MAC 1114 taught by Professor Russel during the Summer '08 term at Valencia.

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