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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!

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1. For the half-angle formula: cos(θ/2) = √((1+cosθ)/2). For θ=2π/3, cos(π/3)=

A) √((1+(−1/2))/2)=√(1/4)=1/2

B) √3/2

C) 1/2

D) √((1−1/2)/2)

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2. What is the reference angle for 290°?

A) 80°

B) 90°

C) 60°

D) 70°

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3. What is sin(−60°)?

A) −1/2

B) 1/2

C) −√3/2

D) √3/2

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4. What is tan(−45°)?

A) 1

B) √2

C) 0

D) −1

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5. What is the exact value of cos(36°)?

A) (√5+1)/4×2

B) (√5+1)/4

C) (1+√5)/4

D) (√5−1)/4

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6. Solve: sin(2x) = cos(x) for x ∈ [0, 2π). How many solutions?

A) 5

B) 4

C) 2

D) 3

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7. What is sin(α+β)−sin(α−β)?

A) 2cosαsinβ

B) 2sinαcosβ

C) 2sinβcosα

D) Both A and B

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8. What is the argument of the complex number 1 + i?

A) π/6

B) π/4

C) π/3

D) π/2

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9. What is sin(A)sin(B)= in terms of cosines?

A) cos(A+B)/2

B) cos(A−B)/2

C) cos(A−B)−cos(A+B))/2

D) (cos(A−B)+cos(A+B))/2

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10. What is arctan(√3)?

A) π/4

B) π/6

C) π/2

D) π/3

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11. The expression sinθ/(1 + cosθ) + (1 + cosθ)/sinθ simplifies to:

A) 2 cot θ

B) 2 csc θ

C) 2 sec θ

D) 2 tan θ

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12. Prove: sec²x + csc²x = sec²x · csc²x.

A) True: LHS = 1/cos²x + 1/sin²x = (sin²x+cos²x)/(sin²xcos²x) = 1/(sin²xcos²x) = sec²x·csc²x

B) Only for x=45°

C) False

D) Only in Q1

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13. For the equation cos(2x)+cosx=0 in [0,2π), find all solutions.

A) 2π/3,4π/3,π... (2cos²x−1)+cosx=0. cosx(2cosx+1)... wait: 2cos²x+cosx−1=0. (2cosx−1)(cosx+1)=0. cosx=1/2:π/3,5π/3. cosx=−1:π. Three solutions: π/3,π,5π/3.

B) π/3,π,5π/3

C) π/2,3π/2

D) π/3,π,5π/3

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14. A clock hand of length 10 cm moves 30°. Arc length swept:

A) π cm... s=rθ=10×(π/6)=5π/3

B) 5π/3 cm

C) 10π/3 cm

D) π/6 cm

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15. What is the exact value of sin(75°)?

A) (√6+√2)/4

B) (√6−√2)/4

C) (√2+√3)/2

D) √3/2

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16. What is the value of tan²(45°) + 1?

A) 3

B) 1

C) 4

D) 2

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17. What is the value of sin²(10°)+sin²(20°)+sin²(30°)+...+sin²(90°)?

A) 9/2

B) 6

C) 11/2

D) 5

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18. The law of cosines with C=90° reduces to:

A) c²=a²+b²−2ab

B) c=a+b

C) a²+b²=c²

D) a/b=sinA/sinB

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19. The function y=2sin(x)+2cos(x) has amplitude:

A) 4

B) 2√2

C) √2

D) 2

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20. A pendulum swings through an arc of 15 cm on a circle of radius 30 cm. The angle subtended in radians is:

A) 1/2

B) 1

C) π/4

D) 2

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21. A ship travels 15km on bearing 90° (due east). How far north does it travel?

A) 15km

B) 10km

C) 5km

D) 0km

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22. Find all θ in [0°,360°): tan(θ)+cot(θ)=2

A) 90° and 270°

B) 45° and 225°

C) 30° and 210°

D) No solution

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23. If f(x)=2sin(3x+π/6)−1, what is the maximum value?

A) 0

B) 1

C) 2

D) 3

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24. What is the value of cos(π/2)?

A) −1

B) 0

C) 1/2

D) 1

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25. What is the value of ∏(cos(π/2ⁿ)) for n=1 to ∞?

A) π/2

B) π

C) 2/π

D) 1/π

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26. The value of tan(π/7)+tan(2π/7)+tan(3π/7) = ?

A) 3√7

B) 7√7/3

C) 7... by identity, the sum=−√7 for the product of roots of a Chebyshev-derived polynomial.

D) √7

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

A) 30°, 150°, 210°, 330°

B) 45°, 135°, 225°, 315°

C) 60°, 120°, 240°, 300°

D) 30°, 150°, 210°, 330°

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28. The midline of y=3sin(x)+4 is:

A) y=3

B) y=1

C) y=4

D) y=7

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29. The equation 2 sin²x − 3 sin x + 1 = 0 has solutions in [0°, 360°):

A) All A and C are equivalent

B) 30°, 90°, 150° only

C) 30°, 90°, 150°

D) sin x = 1 or sin x = 1/2

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30. The function f(x) = tan(x) is undefined at:

A) x = π/4 + nπ

B) x = nπ

C) x = π/2 + nπ

D) x = 2nπ

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