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Unit 2 Review

This document is a review guide for a precalculus unit test on trigonometric functions. It includes definitions and identities involving the six trig functions, the unit circle, Pythagorean identities, sum and difference identities, double angle identities, and solving trigonometric equations. Examples are provided to simplify expressions using identities and to verify identities by showing step-by-step work. Students are asked thinking questions about trigonometric identities and to derive some identities. The final problems involve using a calculator to find solutions to trigonometric equations.

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78 views6 pages

Unit 2 Review

This document is a review guide for a precalculus unit test on trigonometric functions. It includes definitions and identities involving the six trig functions, the unit circle, Pythagorean identities, sum and difference identities, double angle identities, and solving trigonometric equations. Examples are provided to simplify expressions using identities and to verify identities by showing step-by-step work. Students are asked thinking questions about trigonometric identities and to derive some identities. The final problems involve using a calculator to find solutions to trigonometric equations.

Uploaded by

teenwolf4006
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Precalculus Advanced

Unit 6 Test Review Guide Name_______________________

Quick Review of the Unit Circle Six Trig Functions


Label the 1st Quadrant with Standard Values

sin x 


cos x 


tan x  


cot x 


sec x 


csc x 


Reciprocal Identities

  


sec x  sin x  tan x 
  
  
csc x  cos x  cot x 
  

Pythagorean Identities –

1.)

2.)

3.)

Verifying Identities – Guidelines

1.)

2.)

3.)

4.)

5.)

1
Sum & Difference Identities

1.)

2.)

3.)

Double Angle Identities

1.)

2.)

3.)

Simplify the expression.

cot x
1. 2. sin x tan x  cos x
csc x

Verify the expression. Show all steps nice and neatly. Carry the equal sign down.
cos 2 x
3. sec y cos y  1 4.  1  sin x
1  sin x

1
5. cot x  tan x  csc x sec x 6.  csc x  sin x
sec x tan x

2
7. tan 4 x  2 tan 2 x  1  sec4 x 8. sin  (csc  sin  )  cos2 

 
9. sin      cos  10. sec2 x cot x  cot x  tan x
2 

Solve. Find all solutions for problems 11-16.

11. 4cos x  1  2cos x 12. sin x  3  sin x

 
13. cos( x  )  cos( x  )  1 14. 3sec2 x  4
3 3

15. sin(2 )  1  cos(2 ) 16. sec x  1  2 tan 2 x

3
Solve. Find solutions over the interval 0, 2  for problems 17- 19.
17. cos 2 x  3sin x  2 18. sin(2 x)  2 sin x  0

19. tan x  sin x  0

20. Find the exact value for


7
(a) cos(15) (b) sin
12

4
21. Let cos   and  be in quadrant II. Find
5
(Hint: Start by drawing a reference triangle.)
(a) sin 2 (b) cos 2

22. Find the exact value of the trig function given that sin u  5/13 and cos v  3/ 5
Angles u and v are in quadrant II.
(Hint: Start by drawing reference triangles.)
(a) cos(u  v) (b) sin(u  v)

4
Thinking Questions!

23. Use the unit circle to explain why cos2 x  sin2 x  1 is an identity. Is this identity true on any
circle? Use complete sentences. Labeling the picture will help!

24. Explain in one sentence why the sine of any angle of rotation must be in the interval  1,1 .

25. Given the Pythagorean identity cos2 x  sin2 x  1 , derive the two other versions of this identity
for tan 2 x and cot 2 x .

26. Derive the double angle formula for sin 2x .


(Hint: Use the sine of a sum identity.)

5
Calculator

Solve for solutions [0, 2 ) . If something is a standard value, then the answer must be written as a
fraction.

27. 4sin x  3  0 28. cos2 x  sin x  1

Find ALL solutions.

29. cos2 x  2cos x  1  0 30. tan 2 x  6 tan x  5  0

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