How To Solve Inverse Equations

**Inverse trigonometric equations are solved following these steps:**

- Isolate the trig function
- Find the reference angle
- Leave a positive and negative sign in front of the square root function
- Find quadrants
- Calculate the solution(s)

**Examples**

**Ex. 1**

tanx=tan^{-1}(1.256)

tanx = .9 <— Isolate trig function.

II, IV <— Determine quadrants.

II: π - .9 = 2.24 <— Determine solutions.

IV: 2π - .9 = 5.38

**Solutions: {2.24, 5.38}**

**Ex. 2**

tan-1(tan(3π/4))

tan-1(tan(3π/4))

tan(3π/4) <— Isolate trig function.

tan(π/4) <— Determine reference angle.

II <— Determine quadrants.

**Solution: -π/4**

**Practice Problems**

ANSWERS

1) sin(tan^{-1}(1/2))

2) cos(sin^{-1}(1/3))