ACT Math: Trigonometry 3

Question 1

In a right triangle, the two legs measure 6 and 8. What is sin of the angle opposite the leg of length 6?

Accepted Answer

6/10

Answer

The hypotenuse is 10, so sine of that angle is opposite/hypotenuse = 6/10.

Question 2

What is the exact value of tan(45°)?

Accepted Answer

1

Answer

In a 45-45-90 triangle the legs are equal, so tan(45°) = 1.

Question 3

Using the law of sines, if a = 10, sin A = 0.5, and sin B = 0.8, what is side b?

Accepted Answer

16

Answer

b = a · sin B / sin A = 10 · 0.8 / 0.5 = 16.

Question 4

What is the amplitude of y = 3sin(2x)?

Accepted Answer

3

Answer

The amplitude is the coefficient in front of sine, which is 3.

Question 5

Which expression equals sec(θ)?

Accepted Answer

1/cosθ

Answer

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

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