Master ACT Trigonometry Quiz for Exam Success

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30 random questions |30 minutes | Questions are randomized every attempt. Good luck!

ACT Math - Trigonometry Practice Test

Test your ACT trigonometry skills with 30 random practice test questions covering sin, cos, tan, and identities!

1 / 30

1. What is cos(60°)?

A) 1/2

B) 0

C) 1

D) √3/2

Explanation: cos(60°) = 1/2 is a standard trigonometric value

2 / 30

2. What is the inverse cosine of 0?

A) 90°

B) 180°

C) 45°

D) 0°

cos⁻¹(0) = 90° because cos(90°) = 0.

3 / 30

3. In a right triangle, opposite=5 and adjacent=12. What is tan(θ)?

A) 12/5

B) 12/13

C) 5/13

D) 5/12

tan=opposite/adjacent=5/12.

4 / 30

4. What is cos(A-B) when A=90°, B=30°?

A) 1/2

B) 0

C) −√3/2

D) √3/2

cos(60°)=1/2.

5 / 30

5. What is the distance traveled by a point on a circle of radius 5 for an angle of 2π/3?

A) 10π/3

B) 5π

C) 5π/3

D) 10π

s=rθ=5×2π/3=10π/3.

6 / 30

6. What is sin(210°)?

A) √3/2

B) −1/2

C) 1/2

D) −√3/2

Q3, ref=30°. sin negative. sin(210°)=-1/2.

7 / 30

7. What is the exact value of tan(π/3)?

A) √3

B) √3/2

C) 1

D) 1/√3

tan(60°)=sin(60°)/cos(60°)=(√3/2)/(1/2)=√3.

8 / 30

8. What is 1-2sin²(θ) equal to?

A) tan(2θ)

B) cos(2θ)

C) cot(2θ)

D) sin(2θ)

Double angle: cos(2θ)=1-2sin²θ.

9 / 30

9. What is the value of sin(30°)cos(60°)+cos(30°)sin(60°)?

A) cos(90°)=0

B) sin(90°)=1

C) Both A and C

D) 1

sin(30°+60°)=sin(90°)=1. Both A and C correct.

10 / 30

10. What is cos(360°)?

A) 1

B) −1

C) 180

D) 0

cos(360°)=cos(0°)=1.

11 / 30

11. What is 150° in radians?

A) 3π/4

B) 7π/6

C) 5π/4

D) 5π/6

150×π/180=5π/6.

12 / 30

12. What is the reference angle for 330°?

A) 60°

B) 70°

C) 30°

D) 45°

330° is in Q4. Reference angle = 360° - 330° = 30°.

13 / 30

13. Which of the following equals cot(θ)?

A) 1/tan

B) sin/cos

C) tan

D) cos/sin

cot(θ)=cos(θ)/sin(θ)=1/tan(θ). Both B and D are correct, but D is more direct.

14 / 30

14. What is sin(30°)?

A) 1/2

B) 1/√2

C) 1

D) √3/2

Explanation: sin(30°) = 1/2 is a standard trigonometric value

15 / 30

15. What is the period of the tangent function?

A) π

B) π/2

C) 4π

D) 2π

Period of tan(x) = π.

16 / 30

16. How many solutions does sin(x) = 0.5 have in [0°, 360°)?

A) 3

B) 4

C) 1

D) 2

sin = 0.5 at 30° and 150°. Two solutions.

17 / 30

17. What is 2sin(θ)cos(θ) equal to?

A) cos(2θ)

B) sin(2θ)

C) 2

D) tan(2θ)

Double angle formula: sin(2θ)=2sinθcosθ.

18 / 30

18. What is the value of cos(2×30°)?

A) √3/2

B) 0

C) −1/2

D) 1/2

cos(60°)=1/2.

19 / 30

19. What is sin²(x) + cos²(x)?

A) 2

B) 1

C) -1

D) 0

Explanation: This is the Pythagorean identity — always equals 1

20 / 30

20. What is the value of cos(30°)+cos(150°)?

A) 1

B) 0

C) √3/2

D) √3

cos(30°)=√3/2. cos(150°)=-√3/2. Sum=0.

21 / 30

21. What is cos(−60°)?

A) −1/2

B) √3/2

C) −√3/2

D) 1/2

cos is an even function: cos(-θ) = cos(θ). cos(-60°) = cos(60°) = 1/2.

22 / 30

22. What is cos(3π/2)?

A) 1

B) √2/2

C) 0

D) −1

cos(270°)=0.

23 / 30

23. What is the value of arcsin(√3/2)?

A) 30°

B) 45°

C) 90°

D) 60°

sin(60°)=√3/2. arcsin(√3/2)=60°.

24 / 30

24. What is the exact value of cos(π/4)+sin(π/4)?

A) √2

B) 2

C) √2/2

D) 1

cos(π/4)=sin(π/4)=√2/2. Sum=√2/2+√2/2=√2.

25 / 30

25. What is the exact value of sin(2π/3)?

A) -√3/2

B) √3/2

C) 1/2

D) -1/2

2π/3=120°. Q2, reference 60°. sin positive. sin(120°)=√3/2.

26 / 30

26. What is sin(π)?

A) π

B) 1

C) 0

D) -1

sin(π)=sin(180°)=0.

27 / 30

27. What is the vertical shift of y=sin(x+π/3)-2?

A) −π/3

B) π/3

C) 2

D) −2

Vertical shift=-2. Midline: y=-2.

28 / 30

28. What is the reference angle for 135°?

A) 55°

B) 65°

C) 45°

D) 35°

180°-135°=45°.

29 / 30

29. The angle of elevation from a point 30m away to the top of a tree is 60°. How tall?

A) 60

B) 30√3

C) 30/√3

D) 15√3

h=30tan(60°)=30√3.

30 / 30

30. In a right triangle, if tan(θ)=1, what is θ?

A) 30°

B) 45°

C) 60°

D) 90°

tan(45°)=1.

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