Precal Matters
WS 5.3 Circular Trig Functions
Name_________________________________________ Date________________________ Period______
Worksheet 5.3—Circular Trig Functions
Show all work. All answers must be given as either simplified, exact answers. A calculator is not
permitted unless otherwise stated.
Multiple Choice
1. Which of the following trig functions is undefined?
(A) sin 30o
(B) tan 0
(C) cos
π
2
(D) csc90o
2. If θ is the smallest angle in a 3-4-5 right triangle, then sin θ =
3
3
4
(A)
(B)
(C)
5
4
5
(D)
5
4
(E) sec
(E)
3π
2
5
3
3. If a non-horizontal line has a slope of sin θ for some θ , then the line will be perpendicular to a line with
a slope of
(A) cos θ
(B) − cos θ
(C) cscθ
(D) − cscθ
(E) − sin θ
4. Which of the following trig ratios could NOT be π ?
(A) tan θ
(B) cos θ
(C) cot θ
(D) secθ
5. If sin θ = 0.4 , then sin ( −θ ) + cscθ =
(A) −0.15
(B) 0
(D) 0.65
(C) 0.15
Page 1 of 6
(E) cscθ
(E) 2.1
Precal Matters
WS 5.3 Circular Trig Functions
6. If cos θ = 0.4 , then cos (θ + π ) =
(A) −0.6
(B) −0.4
(C) 0.4
7. The range of the function f ( x ) = (sin θ ) + ( cosθ ) is
2
(A) { y y = 1}
(B) { y −1 ≤ y ≤ 1}
8. If secθ = −
13
and tan θ > 0 , then sin θ =
5
12
5
(A) −
(B) −
13
12
9. (Calculator Permitted) Evaluate sec30
(A) 0.5
(B) −1.012
(D) 0.6
(E) 3.54
2
(C) { y 0 ≤ y ≤ 1}
(C)
5
13
(C) undefined
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(D) { y 0 ≤ y ≤ 2}
(D)
5
12
(D) 1.547
(E)
(E) { y y ≥ 0}
12
13
(E) 6.483
Precal Matters
WS 5.3 Circular Trig Functions
10. Evaluate cos
57π
4
(A)
2
2
(B) −
2
2
(C) 1
(D) −1
(E) 0
11. For each of the following angles θ , draw the associated reference triangle, then find the reference
angle. Then find the values for cos θ , sin θ , and tan θ .
2π
5π
5π
(a) θ =
(b) θ =
(c) θ =
3
4
6
(d) θ =
7π
4
(e) θ =
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3π
2
Precal Matters
WS 5.3 Circular Trig Functions
12. Evaluate the following from the Unit Circle.
5π
(a) sin 240o
(b) cos
(c) tan150o
3
(d) csc
π
3
(e) sec
π
2
(f) cot 0
13. (Calculator Permitted) Find the exact value of each of the following trig ratios of angles that are
coterminal with unit circle angles.
⎛ 29131π ⎞
⎛ 674523π ⎞
⎛ 201152010π ⎞
(a) sin ⎜
(b) sec ⎜
(c) csc ⎜
⎟
⎟
⎟
6
3
⎝ 4 ⎠
⎝
⎠
⎝
⎠
⎛ 897513π ⎞
(d) cot ⎜
⎟
6
⎝
⎠
⎛ −8675309π ⎞
(e) cos ⎜
⎟
3
⎝
⎠
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⎛ 643281359π ⎞
(f) tan ⎜
⎟
4
⎝
⎠
Precal Matters
WS 5.3 Circular Trig Functions
14. If the terminal side of θ passes through the given point, find the simplified, exact values of all six trig
functions of θ . THEN, find θ and θ ref if 0o < θ < 360o.
(a) ( −5,3)
(b) ( −4, −5)
15. If cot θ is undefined and secθ < 0 , find the exact values of all six trig functions of θ . THEN, find θ
and θ ref if 0 < θ < 2π .
16. Solve the following equations for 0 ≤ θ < 2π using your Unit Circle knowledge. (There might be
more than one solution for each)
3
1
(a) sin θ = −
(b) tan θ = −1
(c) cot θ =
(d) sec θ = 2
3
2
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Precal Matters
WS 5.3 Circular Trig Functions
17. For θ ∈ [−2π ,4π ] , solve the equation tan θ = 1 if sin θ < 0 .
18. (Calculator Permitted) Evaluate the following to 3 decimals.
(a) sin 257o13"
(b) cos13
5π
(e) csc
6
25π
(d) sec
7
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(
(c) cot −190.3o
o
)