Trigonometry Core Concepts 4

Question 1

In a right triangle with legs 7 and 24, what is the cosine of the angle opposite the leg of length 7?

Accepted Answer

24/25

Answer

The hypotenuse is √(49+576)=25; cosine of that angle = adjacent/hypotenuse = 24/25.

Question 2

What is the exact value of sin(60°)?

Accepted Answer

√3/2

Answer

From the 30-60-90 triangle, sin(60°) = √3/2.

Question 3

The graph of y = sin(2x) compared to y = sin(x) has a period that is:

Accepted Answer

Half as long

Answer

Multiplying x by 2 compresses the period by half: 2π/2 = π.

Question 4

What is the cofunction of sin(30°)?

Accepted Answer

cos(60°)

Answer

Cofunction identity: sin(θ) = cos(90° - θ), so sin(30°) = cos(60°).

Question 5

Which of the following equals sec(θ)?

Accepted Answer

1/cos(θ)

Answer

Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).

Trigonometry Practice Test