Ximpledu

Inverse Trigonometric Function

See how to solve the inverse trigonometric function
(arcsine, arccosine, arctangent).
3 examples and their solutions.

Arcsine

Formula

x = arcsin y
→ sin x = y (-π2 x π2)
Arcsine is the inverse function of sine.
(-π/2 ≤ x ≤ π/2)
So, to solve arcsin y,
1. Set x = arcsin y.
2. Change it to sin x = y.
(-π/2 ≤ x ≤ π/2)
3. Solve the trigonometric equation.

Example

arcsin 32
Solution

Arccosine

Formula

x = arccos y
→ cos x = y (0 ≤ x ≤ π)
Arccosine is the inverse function of cosine.
(0 ≤ x ≤ π)
So, to solve arccos y,
1. Set x = arccos y.
2. Change it to cos x = y.
(0 ≤ x ≤ π)
3. Solve the trigonometric equation.

Example

arccos (-12)
Solution

Arctangent

Formula

x = arctan y
→ tan x = y (-π2 x π2)
Arctangent is the inverse function of tangent.
(-π/2 ≤ x ≤ π/2)
So, to solve arctan y,
1. Set x = arctan y.
2. Change it to tan x = y.
(-π/2 ≤ x ≤ π/2)
3. Solve the trigonometric equation.

Example

arctan (-1)
Solution