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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
Use the following information to answer the next question
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
Use the following information to answer the next question
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
Use the following information to answer the next question
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
Use the following information to answer the next question
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.