Explanation

Inverse trigonometric functions reverse trigonometric functions.

Examples:

• sin⁻¹(x) or arcsin(x)

• cos⁻¹(x) or arccos(x)

• tan⁻¹(x) or arctan(x)

Important:

• sin⁻¹(x) does NOT mean 1 / sin(x)

• It means “the angle whose sine is x”

Example:
sin(π/6) = 1/2
sin⁻¹(1/2) = π/6

Inverse trig functions return angles, not ratios.

Each inverse has a restricted range so it gives only one answer.

Quiz

1. What does sin⁻¹(x) represent?

2. What is sin⁻¹(√2/2)?

3. Is sin⁻¹(x) the reciprocal of sin(x)?

4. Do inverse trig functions output angles or ratios?

5. Why are inverse trig functions restricted?

Answer Key

1. The angle whose sine is x

2. π/4

3. No

4. Angles

5. To make the function one-to-one