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SAT Math - Trigonometry Practice Test

Test your SAT Math - Trigonometry skills with 30 random practice test questions. Great for students preparing for the SAT Math - Trigonometry section!

1 / 30

1. If cos(θ)=−1/2 and sin(θ)<0, what is θ?

A) 240°

B) 120°

C) 210°

D) 150°

2 / 30

2. The double angle formula for cosine: cos(2θ)=1−2sin²(θ). What is cos(2θ) when sin(θ)=4/5?

A) 7/25

B) 17/25

C) −17/25

D) −7/25

3 / 30

3. The number of revolutions per minute of a wheel with angular velocity 120π rad/min:

A) 90

B) 120

C) 30

D) 60

4 / 30

4. The value of cos(π/9)cos(2π/9)cos(4π/9) =

A) 1/4

B) 1/2

C) 1/8

D) √3/8... using product formula: ∏cos(2^k·θ)=sin(2^n·θ)/(2^n·sinθ). n=3,θ=π/9: sin(8π/9)/(8sin(π/9))=sin(π/9)/(8sin(π/9))=1/8.

5 / 30

5. What is the value of tan(π)?

A) −1

B) undefined

C) 0

D) 1

6 / 30

6. The equation cos(x)=cos(y) implies:

A) x=−y

B) x+y=π

C) x=2nπ±y

D) x=y

7 / 30

7. Given the triangle with a=7, b=7, A=45°. How many triangles are possible?

A) 1

B) 0

C) 2

D) Infinitely many

8 / 30

8. The number of real solutions to tan(x)=x is:

A) 5... One solution is x=0. There are infinitely many (one per period beyond each asymptote).

B) 1

C) Infinitely many

D) 3

9 / 30

9. For y = 3sin(x) + 2, the range is:

A) [−3, 3]

B) [0, 5]

C) [−1, 5]

D) [2, 5]

10 / 30

10. What is the value of 2sin(45°)cos(45°)?

A) 2

B) √2

C) √2/2

D) 1

11 / 30

11. The period of y = cos(x/3) is:

A) 6π

B) 2π

C) π

D) 9π

12 / 30

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

A) √3

B) 1

C) (1+√3)

D) (1+√3)/2

13 / 30

13. For f(x) = 5 cos(3x − π) + 2, what is the amplitude?

A) 5

B) 2

C) 3

D) 7

14 / 30

14. Using the product-to-sum formula, cos 5x · cos 3x =

A) cos 8x + cos 2x

B) ½[cos 8x + cos 2x]

C) ½[cos 8x − cos 2x]

D) ½[cos 2x − cos 8x]

15 / 30

15. The inverse tangent addition formula: arctan(x)+arctan(y)= arctan((x+y)/(1−xy)) when:

A) Always

B) xy=1

C) xy>1

D) xy<1

16 / 30

16. For f(x) = 2 cos²x − 1, the period is:

A) π

B) π/2

C) 4π

D) 2π

17 / 30

17. How many degrees in one radian (approximately)?

A) 90°

B) 57.3°

C) 180°

D) 45°

18 / 30

18. The value of sin 6° · sin 42° · sin 66° · sin 78° =

A) 1/16

B) 1/8

C) √3/16

D) 3/16... using product formula for multiples

19 / 30

19. What is the value of cos(330°)?

A) 1/2

B) −√3/2

C) −1/2

D) √3/2

20 / 30

20. An angle of 5 radians is approximately:

A) 300°

B) 286°

C) 270°

D) 260°

21 / 30

21. Solve: 3tan²x − 1 = 0 in [0°, 360°).

A) 45°, 135°, 225°, 315°

B) 30°, 150°, 210°, 330°

C) 60°, 120°, 240°, 300°

D) 30°, 150°, 210°, 330°

22 / 30

22. The area of a triangle with a=8, b=6, and included angle C=30° is:

A) 24

B) 12

C) 48

D) 16

23 / 30

23. For the Dottie number d (fixed point of cosine), cos(d)=d. The value d satisfies:

A) d≈0.739

B) d=π/4

C) Both A and B

D) d is a zero of cosx-x

24 / 30

24. For f(x) = 4cos(x/2 − π/4), the period and phase shift are:

A) 4π and π/2 left

B) 4π and π/4 right

C) 4π and π/2 right

D) 2π and π/4 right

25 / 30

25. If sinα+sinβ=a and cosα+cosβ=b, what is cos(α−β)?

A) (a²+b²)/2−1

B) (a²+b²−2)/2

C) a²+b²−1

D) Both A and B

26 / 30

26. What is the value of sec²(30°)?

A) 3/4

B) 4/3

C) 2

D) 4

27 / 30

27. Find all x in [0,2π): sinx·cosx = 1/4.

A) π/3, 2π/3

B) π/12, 5π/12, 13π/12, 17π/12

C) π/4, 3π/4

D) π/6, 5π/6

28 / 30

28. The value of tan 20° + tan 40° + √3 tan 20° tan 40° =

A) √3

B) 1

C) 2√3

D) 3

29 / 30

29. What is 1+tan²(θ) equal to?

A) csc²(θ)

B) sin²(θ)

C) cos²(θ)

D) sec²(θ)

30 / 30

30. What is arccos(1)?

A) 0

B) π/6

C) π/2

D) π/4

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