5.3 Solving Trigonometric Equations Use standard algebraic techniques like collecting like terms and factoring.

Example 1: Solving a Trig Equation Isolate the trig function Use an inverse function

Multiple solutions But p/3 is not the only angle that will make the equation work!

Multiple Solutions But that’s still not it!! The sine and cosine functions have a period of 2π. So every interval of 2π, the solutions repeat. The total solutions are: and

Example 2: Collect Like Terms

Example 3: Extracting Square Roots Solve on the interval [0, 2π) Isolate the trig function Use an inverse function

Example 4: Quadratic Types If an equation looks quadratic, FACTOR IT!! Keep in mind that sine and cosine must be less than 1!

Example 5: Rewriting as one function

Example 6: Squaring/Converting

You Try It!

Graphical Solutions on [0, 2π)

Homework: Page 376 #25, 36, 37, 39, 49, 51, 53