Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Assessment Exemplars: Trigonometry

1. The angle 26π

24, converted to degrees, is _______ °

____ 2. An angle, in radians, that is co-terminal with 30° is

a. −5π

6b. −

13π

6c.

7π

6d.

25π

6

Use the following information to answer the next question

3. The two statements above that are correct are numbered _____ and _____ .

Use the following information to answer the next question

If the point P 0.2,kÊËÁÁ ˆ

¯˜̃ lies on a circle with a radius of 1, then the exact value of k can be

expressed as ± b .

4. The value of b, to the nearest hundredth, is _____ .

5. On a unit circle, if the point P −5

13,12

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ lies on the terminal arm of an angle in standard

position, what are the exact values of the 6 trigonometric ratios?

Name: ________________________ ID: A

2

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6. The values of b, c, d, and e are, respectively, ____, ____ , ____ , and ____ .

____ 7. Which of these values of x is NOT a solution of the equation 3 csc x = − 2?

a. x =7π

6c. x =

4π

3

b. x =−π

3d. x =

5π

3

____ 8. The coordinates of the point that lies at the intersection of the terminal arm and the unit circle at an angle of

213° are

a. (–0.54, –0.84) c. (–0.84, 0.65)

b. (0.65, –0.54) d. (–0.84, –0.54)

9. Given that csc θ = −8

5, where π < θ <

3π

2, determine the exact value of tanθ

10. Determine the exact value of sin −π

6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ + cos

7π

4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

Name: ________________________ ID: A

3

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11. The values of a and b are, respectively, _____ and _____ .

Use the following information to answer the next question

12. Use the following code to indicate that the value of the ratio is zero, or that the ratio is undefined.

1 = The value of the ratio is zero.

2 = The ratio is undefined.

Name: ________________________ ID: A

4

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13. The two statements that are true from the list above are numbered ____ and ____ .

14. For the function y = acos θ + d , the range is −4,10ÈÎÍÍÍ

˘˚˙̇̇ . What are the values of a and d?

15. SE: For the function y = sin 3x + π( ) + 7, what is the phase shift and period of the corresponding graph?

16. Given that f θ( ) = cos nθ( ) has the same period as the graph of g θ( ) = tan θ( ) , the value of n is ______ .

Name: ________________________ ID: A

5

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17. What are the value of a, b, and d?

.

Use the following information to answer the next question

____ 18. The number of true statements about the graph of y = f x( ) from the list above is

a. 1 b. 2 c. 3 d. 4

Name: ________________________ ID: A

6

Use the following information to answer the next question

19. SE: Write an equation for the height of the particular point on the Ferris wheel, h, as a function of time, t, in

the form y = a cos b t − c( )ÊËÁÁ ˆ

¯˜̃

È

ÎÍÍÍÍ

˘

˚˙̇˙̇ + d

20. Solve for θ , where 0° < θ < 360°, in the equation 2cos2θ + cos θ = 0

.

21. SE: For the equation 2cos2θ + sinθ − 1 = 0, final all values for θ that satisfy this equation.

.

.

____ 22. SE: The expression cotx + csc x

sec x + 1, where sec x ≠ 1, is equivalent to

a. sinx b. tanx c. csc x d. cotx

Name: ________________________ ID: A

7

23. Determine the smallest positive value of θ that satisfies the following equation

2 − 3 sec θÊ

ËÁÁÁ

ˆ

¯˜̃˜ sec θ + 3( ) = 0. Round your answer to the nearest degree.

24. SE: Find the general solution to the equation sin 2θ( ) − cos θ = 0=. Express the solution in degrees.

.

Use the following information to answer the next question

25. When the numerical values of the simplified expressions are arranged in ascending order, the expression

numbers are ____ , ____ , ____ , and ____ .

26. SE: What is the exact value of tan5π

12?

.

27. SE: Prove algebraically that 2tanx

1 − tan2x

=sin 2x( )

cos2x − sin

2x

, where x ≠π

4+

π

2n,n ∈ I

,

ID: A

1

Assessment Exemplars: Trigonometry

Answer Section

1. 195°

2. D

3. 13 or 31

4. 0.96

5.

6. 1330

7. A

8. D

9. tanθ =5

39=

5 39

39

10. −1

2+

2

2=

2 − 1

2

11. a = 7, b = 12

12. 2112

13. 14

14. a = 7, d = 3

15. The phase shift is: π

3 to the left, the period is

2π

3

16. 2

17. a = 5, b = 2, d = 3

18. C

19.

ID: A

2

20.

21. sinθ = −1

2 or sinθ = 1 so: θ =

π

2+ 2πn,

7π

6+ 2πn,

11π

6+ 2πn: n ∈ I

22. D

23. θ = 30°

24.

25. 1342

26.

27.