4.2 Solving More Complex Trigonometric Equations

**In this section,**

We will be covering how to solve more complex equations. This section Section 4.1 teaches (4.1 Solving Simple Trigonometric Equations) used for solving the equation, but in addition, it covers setting the equation equal to the function.

**These 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**

3tan^{2}x-1=0

tan^{2}x=⅓

√tan2x=√⅓

tanx=√1/√3

tanx=±√3/3

I,II,III,IV ←Find the quadrants

Reference Angle: π/6 ←Determine reference angle

I: π/6 ←Determine solutions

II: 5π/6

III:7π/6

IV:11π/6

**Solutions: {π/6, 5π/6, 7π/6, 11π/6}**

**Ex. 2**

tan^{2}x-3=0

tan^{2}x=3

tanx=+/-√3

tanx=+√3 or -√3 ←Find the quadrants

x=π/3

x=2π/3

**Solutions: {π/3, 2π/3}**

**Practice problems:**

1) 2cos2x = ½

2) sin2(2x)=3/4