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 the period of y=tan(x/4)?

A) π/4

B) π

C) 2π

D) 4π

Period=π/(1/4)=4π.

2 / 30

2. What is 7π/6 in degrees?

A) 200°

B) 230°

C) 210°

D) 220°

7π/6×180/π=210°.

3 / 30

3. What is sin(2θ) when sinθ=3/5 (Q1)?

A) 12/25

B) 24/25

C) 6/25

D) 7/25

cosθ=4/5. sin(2θ)=2sinθcosθ=2(3/5)(4/5)=24/25.

4 / 30

4. What is the value of cos(π)?

A) 0

B) -1

C) 1

D) π

cos(π) = cos(180°) = -1.

5 / 30

5. What is the horizontal shift of y=cos(x-π)?

A) Down by π

B) Left by π

C) Right by π

D) Up by π

x-π shifts right by π.

6 / 30

6. In a right triangle with angle 37°, adjacent=24. What is the hypotenuse? (cos37°≈0.8)

A) 30

B) 20

C) 32

D) 25

cos(37°)=adj/h=24/h=0.8. h=30.

7 / 30

7. What is sin(5π/6)?

A) √3/2

B) 1/2

C) −√3/2

D) −1/2

5π/6=150°. Q2, ref=30°. sin positive. sin=1/2.

8 / 30

8. What is the period of the tangent function?

A) 4π

B) π

C) π/2

D) 2π

Period of tan(x) = π.

9 / 30

9. Two sides and included angle: a=5, b=7, C=60°. What is c using Law of Cosines?

A) √(59)

B) √(29)

C) √(39)

D) √(49)

c²=a²+b²-2ab cosC = 25+49-2(5)(7)(0.5) = 74-35 = 39. c=√39.

10 / 30

10. What is the inverse sine of 1?

A) 0°

B) 30°

C) 60°

D) 90°

sin⁻¹(1) = 90° because sin(90°) = 1.

11 / 30

11. What is the period of y = cos(2πx)?

A) 2

B) 1

C) 2π

D) π

Period = 2π/b = 2π/(2π) = 1.

12 / 30

12. What is the inverse cosine of (-1)?

A) 270°

B) 0°

C) 90°

D) 180°

cos(180°)=-1. arccos(-1)=180°.

13 / 30

13. In a right triangle with hypotenuse 10 and opposite side 5, what is sin(θ)?

A) 1/2

B) 5

C) 2

D) √3/2

Explanation: sin(θ) = opposite/hypotenuse = 5/10 = 1/2

14 / 30

14. Which trigonometric function is equal to adjacent/hypotenuse?

A) sin

B) tan

C) sec

D) cos

Explanation: CAH = Cosine is Adjacent over Hypotenuse

15 / 30

15. In a triangle with sides 7, 8, 9, which angle is opposite the side 9?

A) Smallest

B) Middle

C) Right angle

D) Largest

Largest side is opposite largest angle.

16 / 30

16. What is 5π/4 in degrees?

A) 210°

B) 200°

C) 225°

D) 240°

5π/4×180/π=225°.

17 / 30

17. In which quadrants is cosine negative?

A) II and III

B) I and II

C) III and IV

D) I and IV

Cosine (x-coordinate) is negative in Q2 and Q3.

18 / 30

18. In a 3-4-5 right triangle, what is sin of the largest acute angle?

A) 3/5

B) 5/4

C) 3/4

D) 4/5

Largest acute angle is opposite longest leg=4. sin=4/5.

19 / 30

19. In a right triangle, sin(A)=cos(B). What is A+B?

A) 60°

B) 90°

C) 180°

D) 45°

sin(A)=cos(B)=sin(90°-B). A=90°-B. A+B=90°.

20 / 30

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

A) √3

B) −√3

C) 0

D) 1

−√3/2+√3/2=0.

21 / 30

21. In a right triangle with angle 60° and adjacent side 5, what is the hypotenuse?

A) 5√3

B) 10√3

C) 10

D) 5/2

cos(60°)=1/2 = adjacent/hypotenuse = 5/h → h = 10.

22 / 30

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

A) 90°

B) 30°

C) 60°

D) 45°

tan(45°)=1.

23 / 30

23. In a triangle, a=10, b=12, c=15. Which angle is largest?

A) They are equal

B) Angle opposite b

C) Angle opposite a

D) Angle opposite c

The largest angle is opposite the largest side c=15.

24 / 30

24. What is tan(60°)?

A) 1/√3

B) 1

C) √3/2

D) √3

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

25 / 30

25. What is the value of tan(θ) if sin(θ)=3/5 and θ is in Q1?

A) 3/5

B) 4/3

C) 3/4

D) 4/5

cos=√(1-9/25)=4/5. tan=sin/cos=(3/5)/(4/5)=3/4.

26 / 30

26. What is cos(270°)?

A) -1

B) 0

C) √2/2

D) 1

At 270°, point is (0,-1). cos=x-coord=0.

27 / 30

27. What is the exact value of sin(π)?

A) π

B) 1

C) -1

D) 0

sin(π)=sin(180°)=0.

28 / 30

28. A pendulum swings through an angle of π/6 radians. If its length is 9m, what is the arc length?

A) 3π/2

B) π

C) 9π/6=3π/2

D) 2π

s=rθ=9×π/6=3π/2.

29 / 30

29. What is the formula for the angle between two vectors using dot product?

A) cos(θ)=(a·b)/(|a||b|)

B) sin(θ)=(a·b)/(|a||b|)

C) cos(θ)=|a||b|/(a·b)

D) tan(θ)=a·b

cos(θ)=(a·b)/(|a||b|).

30 / 30

30. What is the value of sin(θ)×csc(θ)?

A) 1

B) csc²θ

C) sin²θ

D) 0

sinθ×1/sinθ=1.

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