Trigonometry Inverse Functions 2

Question 1

What is the range of arcsin(x)?

Accepted Answer

[-π/2, π/2]

Answer

arcsin(x) outputs values in [-π/2, π/2] to make it a proper function.

Question 2

Evaluate arctan(√3).

Accepted Answer

π/3

Answer

tan(π/3) = √3, so arctan(√3) = π/3.

Question 3

Which of the following is NOT in the domain of arccos(x)?

Accepted Answer

2

Answer

arccos(x) is only defined for x in [-1, 1], so x = 2 is outside the domain.

Question 4

Find the exact value of sin(arccos(3/5)).

Accepted Answer

4/5

Answer

Using a 3-4-5 right triangle, if cos θ = 3/5 then sin θ = 4/5.

Question 5

What is the range of arccot(x)?

Accepted Answer

(0, π)

Answer

arccot(x) is conventionally defined with range (0, π), excluding the endpoints.

Trigonometry Practice Test