Penn Foster Trigonometry exam

1

1. Find the complete exact solution of sin x = .

2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places.

3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places.

− 3

2

E x a m in a t io n

E x a m in a t io n

Trigonometric Functions

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Questions 1–20: Answer the following questions.

EXAMINATION NUMBER

00769700

Examination2

4. Prove that tan2 � – 1 + cos2 � = tan2 � sin2 �.

5. Prove that tan � sin � + cos � = sec �.

6. Prove that = cos � + sin �.

7. Prove that .

8. Prove that = cos � – cot � cos �.

9. Find a counterexample to shows that the equation sec � – cos � = sin � sec � is not an identity.

sin cos

tan sin cos tan

2 2ω ω ω ω ω ω

− +

1 + tan

1 tan

sec + 2tan

1 tan

2

2

θ θ

θ θ θ− −

=

tan cos + sin

sin

2 2λ λ λ λ

Examination 3

10. Write tan as a function of � only.

11. Write cos as a function of � only.

12. Write cos(–83°) as a function of a positive angle.

13. Write sin(125°) in terms of its cofunction. Make sure your answer is a function of a positive angle.

14. Find the exact value of sin(195°).

15. Sketch a graph of y = sin(–2x), paying particular attention to the critical points.

λ π

+ 3

⎛ ⎝ ⎜⎜⎜

⎞ ⎠ ⎟⎟⎟⎟

π β

4 −

⎛ ⎝ ⎜⎜⎜

⎞ ⎠ ⎟⎟⎟⎟

2

4

–4

–2 π 2π

Examination4

16. If cot 2� = with 0 � 2� � �, find cos�, sin�, and tan�.

17. Find the exact value of sin2� if cos� = (� in Quadrant I).

18. Find the exact value of tan2� if sin� = (� in Quadrant II).

19. Solve sin 2x + sin x = 0 for 0 � x � 2�.

20. Write 2sin37°sin26° as a sum (or difference).

5

12

4

5

5

13