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Pre-Calculus Test On Chapter 5 Analytic Trigonometry Date: - Name: - Period

1. Verify several trigonometric identities involving sin, cos, tan, sec, and csc functions. 2. Use angle addition, difference, and half-angle identities to evaluate trigonometric functions of sums, differences, and halves of angles. 3. Choose the correct expression equivalent to (sec u + 1)(sec u - 1) and the expression that could not be set equal to sin x from multiple choice options involving trigonometric functions of angles, sums, differences, and inverses.

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Ishaan Verma
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173 views3 pages

Pre-Calculus Test On Chapter 5 Analytic Trigonometry Date: - Name: - Period

1. Verify several trigonometric identities involving sin, cos, tan, sec, and csc functions. 2. Use angle addition, difference, and half-angle identities to evaluate trigonometric functions of sums, differences, and halves of angles. 3. Choose the correct expression equivalent to (sec u + 1)(sec u - 1) and the expression that could not be set equal to sin x from multiple choice options involving trigonometric functions of angles, sums, differences, and inverses.

Uploaded by

Ishaan Verma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Pre-Calculus Test on Chapter 5 Analytic Trigonometry Date: _ ________

Name: ___________________________ Period: _______

Verify the following trigonometric identities:

1+ sin x
1. 1+ sin 2Θ = (sin Θ + cos Θ) 2 2. tan 2 x + 1 + tan x sec x =
cos2 x

cos Θ cos Θ
3. sin x – sin x cos 2 x = sin 3x 4. − = 2 tan Θ
1−sin Θ 1+ sinΘ

cos Θ
5. tan 2 Θ = csc2 Θ tan 2 Θ – 1 6. tan u + = sec u
1+ sinΘ
Pre-Calculus Test on Chapter 5 Page Two
Use the angle addition and/or difference identities to find the exact value of each function:

7. sin 95°cos 55° + cos 95°sin55° 8. tan 345°

π
9. cos 375° 9. sin
12

Use the half -angle identity to find each value:


π 5π
11. tan 12. cos
8 8

Multiple Choice:
13. A simpler expression for (sec u + 1)( sec u – 1) is A) sin 2 u B) cos 2 u C) tan 2 u
D) cot 2 u E) sec 2 u

π π
14. Which of the following could NOT be set equal to sin x? A) cos ( -x) B) cos (x- )
2 2

C) √ cos2 x−1 D) tanx sec x E) –sin (-x)


15. sin 15° = A) 1/4 B)
√3 C)
√3+ √2 D)
√ 6−√ 2 E)
4 4 4
√6 +√ 2
4

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