FREE ACT Math: Trigonometry Questions and Answers

Question 1

In the right triangle ΔABC, the right angle is at C. If the length of side AC is 12 and the length of the hypotenuse AB is 13, what is the value of cos(A)?

Accepted Answer

12/13

Answer

5/13

Answer

5/12

Answer

13/12

Question 2

What is the exact value of tan(5π/4) on the unit circle?

Accepted Answer

1

Answer

-1

Answer

√2/2

Answer

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Question 3

If sin(θ) = 3/5 and θ is in Quadrant II, what is the value of cos(θ)?

Accepted Answer

-4/5

Answer

4/5

Answer

3/4

Answer

-3/5

Question 4

What is the period of the function f(x) = 3sin(4x)?

Accepted Answer

π/2

Answer

4π

Answer

2π

Answer

3

Question 5

If sec(θ) = -2 and tan(θ) > 0, what is the value of sin(θ)?

Accepted Answer

-√3/2

Answer

1/2

Answer

√3/2

Answer

-1/2

Question 6

A ladder leans against a vertical wall, making an angle of 60° with the ground. If the base of the ladder is 5 feet from the wall, what is the length of the ladder?

Accepted Answer

10 feet

Answer

5√3 feet

Answer

10√3/3 feet

Answer

5/2 feet

Question 7

The expression (tan(x) * csc(x)) / sec(x) is equivalent to which of the following?

Accepted Answer

1

Answer

sin(x)

Answer

cos(x)

Answer

tan²(x)