College Math Placement Test Trigonometry 4

Question 1

A 20-foot ladder leans against a wall at an angle of 60° with the ground. How high up the wall does the ladder reach?

Accepted Answer

10√3 ft

Answer

height = 20 × sin 60° = 20 × (√3/2) = 10√3 feet.

Question 2

What is the exact value of csc(30°)?

Accepted Answer

2

Answer

csc 30° = 1/sin 30° = 1/(1/2) = 2.

Question 3

Which of the following is true for all angles θ?

Accepted Answer

1 + tan²θ = sec²θ

Answer

Dividing sin²θ + cos²θ = 1 by cos²θ gives tan²θ + 1 = sec²θ.

Question 4

What is the phase shift of y = sin(x − π/4)?

Accepted Answer

π/4 to the right

Answer

y = sin(x − π/4) shifts the graph π/4 units to the right.

Question 5

In a right triangle, if one acute angle is θ, then the other acute angle is

Accepted Answer

90° − θ

Answer

The two acute angles in a right triangle sum to 90°, so the other angle is 90° − θ.

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