AMC12 Trigonometry

Question 1

What is sin(30°)?

Accepted Answer

1/2

Answer

sin(30°) = 1/2, a standard value from the 30-60-90 triangle.

Question 2

What is cos(π)?

Accepted Answer

−1

Answer

cos(π) = −1 since π radians corresponds to 180°.

Question 3

Simplify sin²(θ) + cos²(θ).

Accepted Answer

1

Answer

The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for all θ.

Question 4

What is the period of y = sin(2x)?

Accepted Answer

π

Answer

The period of sin(bx) is 2π/b = 2π/2 = π.

Question 5

In a right triangle with hypotenuse 10 and one angle 30°, the side opposite that angle has length:

Accepted Answer

5

Answer

Opposite = hypotenuse × sin(30°) = 10 × 1/2 = 5.

AMC12 - American Mathematics Competition 12 Practice Test