Trigonometry Inverse Functions 3

Question 1

Evaluate arccos(-1/2).

Accepted Answer

2π/3

Answer

cos(2π/3) = -1/2 and 2π/3 is in [0, π], so arccos(-1/2) = 2π/3.

Question 2

If arctan(x) = π/4, what is x?

Accepted Answer

1

Answer

tan(π/4) = 1, so x = 1.

Question 3

What is the domain of arctan(x)?

Accepted Answer

(-∞, ∞)

Answer

The tangent function is defined for all real inputs, so arctan(x) accepts all real x.

Question 4

Evaluate arcsin(-√2/2).

Accepted Answer

-π/4

Answer

sin(-π/4) = -√2/2 and -π/4 is in [-π/2, π/2], so the answer is -π/4.

Question 5

Which expression equals tan(arcsin(x)) for |x| < 1?

Accepted Answer

x/√(1-x²)

Answer

If sin θ = x, then cos θ = √(1-x²), so tan θ = x/√(1-x²).

Trigonometry Practice Test