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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