H. Pre-Calc: REVIEW, Trigonometry
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1 H Pre-Calc: REVIEW, Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question 1 Given and, find and a c, b, d,, 2 What basic trigonometric identity would you use to verify that cot x sin x = cos x? a c b d 3 What basic trigonometric identity would you use to verify that? a sin x = cos x tan x c b d 4 Find sec x if a b c d 5 Find cos x if sin x cot x = 4 a 4 b c 1 d No Solution
2 6 Find cos x if a 1 b 2 c 1 d 0 7 Find the exact value of cos 15 a b c d 8 If and are the measures of two first quadrant angles and sin and sin, find sin ( + ) a b c d 9 Which sum or difference identity would you use to verify that sin (90 + ) = cos? a cos ( ) = cos cos + sin sin b sin ( ) = sin cos + cos sin c sin ( ) = sin cos cos sin d cos ( ) = cos cos sin sin 10 If and terminates in the fourth quadrant, find the exact value of tan 2 a b c d 11 Use a half-angle identity to find the exact value of tan 105 a c b d
3 12 Which double-angle or half-angle identity would you use to verify that? a c b d 13 Solve for a 150 b 30 c 60 d Solve for all real values of x a c b d Short Answer 15 If is between and find Enter the missing value in the below answer: = 16 Find a numerical value of csc x if Enter the missing value in the following answer: 17 Find cos x if
4 18 Find the exact value of sin 15 Enter the missing value in the following answer: 19 If and are the measures of two first quadrant angles and and, find 20 If and q terminates in the third quadrant, find the exact value of sin2q Enter the missing value of the following answer: 21 If and terminates in the first quadrant, find the exact value of sin 2 22 Solve = 0 for Choose all the correct answers in alphabetical order by choice a) 0 b) 30 c) 45 d) 60 e) 90 f) 120 g) 135 h) 160 i) Solve for 24 Solve for Enter the missing value for the following answer:
5 Verify the identity Do not cross the equality 25 Verify that is an identity 26 Verify that is an identity 27 Verify that sin ( + ) = sin is an identity
6 28 Verify that is an identity 29 Verify that cos (270 ) = sin is an identity
7 H Pre-Calc: REVIEW, Trigonometry Answer Section MULTIPLE CHOICE 1 ANS: A TOP: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities, and opposite-angle identities 2 ANS: B TOP: Use the basic trigonometric identities to verify other identities 3 ANS: C TOP: Use the basic trigonometric identities to verify other identities 4 ANS: D TOP: Find the numerical values of trigonometric functions 5 ANS: D TOP: Find the numerical values of trigonometric functions 6 ANS: C TOP: Find the numerical values of trigonometric functions 7 ANS: B TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 8 ANS: A TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 9 ANS: B TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 10 ANS: B TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 11 ANS: A TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 12 ANS: D TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 13 ANS: D TOP: Solve trigonometric equations and inequalities 14 ANS: D TOP: Solve trigonometric equations and inequalities SHORT ANSWER 15 ANS: TOP: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities, and opposite-angle identities 16 ANS: TOP: Find the numerical values of trigonometric functions 17 ANS:
8 TOP: Find the numerical values of trigonometric functions 18 ANS: TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 19 ANS: TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 20 ANS: TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 21 ANS: TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 22 ANS: 0, 120, 180 TOP: Solve trigonometric equations and inequalities 23 ANS: 90 TOP: Solve trigonometric equations and inequalities 24 ANS: TOP: Solve trigonometric equations and inequalities 25 ANS:
9 TOP: Use the basic trigonometric identities to verify other identities 26 ANS: TOP: Use the basic trigonometric identities to verify other identities 27 ANS: TOP: Use the sum and difference identities for the sine, cosine, and tangent functions 28 ANS: TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions 29 ANS: TOP: Use the sum and difference identities for the sine, cosine, and tangent functions
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