4.1 Solving Simple Trigonometric Equations

**In this section,**

You will be learning how to solve simple trigonometric equations. This section relies heavily on the use of reference angles, which we have already memorized!

**These equations are solved following four steps:**

- Isolate the trigonometric function.
- Determine the quadrants in which the reference angle will land in.
- Find the reference angle.
- Calculate the solution(s).

**Examples:**

**Ex. 1**

cosx = √2/2

I, IV x = π/4 ← Determine quadrants reference angles.

I: π/4 ← Reference angle falls in first quadrant.

IV: 2π - π/4 = 7π/4 ← Subtract reference angle from 2π because fourth quadrant equals 2π.

**Solutions: {π/4, 7π/4}**

**Ex. 2**

√3 tanx - 1 = 0

+ 1 + 1 ← Add 1 to both sides of equation.

√3 = 1 ← Divide both sides of equation by √3.

√3 √3

tanx = 1/√3

I, III x = π/6 ← Determine reference angles.

I: π/6 ← Determine solutions.

III: π + π/6 =

6(π + π/6) = ← Find common denominator.

6π/6 + π/6 = 7π/6

**Solutions: {π/6, 7π/6}**

**Practice Problems:**

ANSWER KEY

1) 3sinx + 2 = 0

2) sinθ = √2/2