Solving Trigonometric Equations

Dr. Barry Shildneck Fall 2014

Basic Trig Equations

1) Solve for the trig function (Isolate each trig function in the problem).

2) Ask yourself, “For what angle(s) (between 0 and 2π does this function have this value?”

3) Write those answers down.

4) Find the pattern of solutions as you rotate around the unit circle, if you need the

“general” solution.

Example 1 Solve the equation.

2sin 1 0x

Example 2 Solve the equation on [0, 2π).

sin 2 sinx x

Example 3 Solve the equation.

23tan 1 0x

Example 4 Solve the equation.

2tan sin tanx x x

Example 5 Solve the equation.

22cot cos cotx x x

Basic Quadratic Trig Equations

1) Begin by solving just like you would any general quadratic (but for the

trig functions). - - - - This means set equal to zero and FACTOR!

2) Set each factor equal to zero and solve each equation.

3) Write all of your answers down.

4) Find the pattern of solutions as you rotate around the unit circle, if you need the

“general” solution.

Example 6 Solve the equation on [0, 2π).

22sin sin 1x x

Example 7 Solve the equation.

22sin 3cos 3 0x x

Example 8 – Type number III! Solve the equation on [0, 2π).

cos 1 sinx x

ASSIGNMENT

Alternate Text

P. 376 #3-56(m3)