Solving Trig Equations

In terms of equations like sinx = 0.9

Process

1. Keep the interval in the back of your mind. Usually $0<x<2\pi$. This may change
2. Rearrange all to one side
3. Split into cases of angles. Usually answers will only have 2 angles, but more may occur due to:
   • Interval
   • If trig function is higher exponent than 1.
   • If coefficient in trig function. If you have an equation like sin2x = 0.8, then you are able 2x to coterminal aswell before converting 2x into x to get more answers
4. if its a special angle, easy to find
   • If its not a special angle use Inverse Trigonometric Functions
5. Find the alternative angle through quadrants. if there are 2 angle gotten from square rooting, then you have 4 solutions

Double Angles

Example

sin2x = $\frac{\sqrt{3}}{2}$

2x is in quadrant 1 and 2. 2x = $\frac{\pi }{3}+2\pi k$ 2x = $\frac{2\pi }{3}+2\pi k$ lets do the first case first x = $\frac{\pi +6\pi k}{6}$ k = 0: x = $\frac{\pi }{6}$ k = 1: x = $\frac{7\pi }{6}$ onto the second case x = $\frac{2\pi +6\pi k}{3}$ k = 0: x = $\frac{\pi }{3}$ k = 1: x = $\frac{4\pi }{3}$

x ∈ {$\frac{\pi }{6},\frac{7\pi }{6},\frac{\pi }{3},\frac{4\pi }{3}$}