MPT Trigonometry

Question 1

What is the value of sin(30°)?

Accepted Answer

1/2

Answer

The sine of 30° is a standard trigonometric value:
sin(30°) = 1/2.

Question 2

Which of the following is the correct identity for cos²(θ) + sin²(θ)?

Accepted Answer

1

Answer

The Pythagorean identity states that:
cos²(θ) + sin²(θ) = 1, which is a fundamental trigonometric identity.

Question 3

Solve for θ: tan(θ) = 1

Accepted Answer

θ = 45°

Answer

The tangent of 45° is 1 because tan(45°) = sin(45°) / cos(45°) = 1/1 = 1.

Question 4

What is the value of cos(π/3)?

Accepted Answer

1/2

Answer

cos(π/3) corresponds to cos(60°), and the value of cos(60°) is 1/2.

Question 5

If sin(θ) = 3/5, what is cos(θ) when θ is in the first quadrant?

Accepted Answer

4/5

Answer

Use the Pythagorean identity:
sin²(θ) + cos²(θ) = 1.
(3/5)² + cos²(θ) = 1,
9/25 + cos²(θ) = 1,
cos²(θ) = 1 - 9/25 = 16/25,
cos(θ) = √(16/25) = 4/5.

(MPT) UCF Math Placement Test Practice Test