5.3 Solving Trigonometric Equations Turn in your Worksheet on Simplifying Trig Expressions if you haven’t yet. Objective: In this lesson you will be learning how to solve trigonometric equations To solve a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation, then find all values of the variable for which the equation is true.

5.3 Solving Trigonometric Equations Find all of the solutions of in the interval

5.3 Solving Trigonometric Equations Solve: Original equation Add 1 to each side Divide each side by 2 But, you were asked to find all solutions, not just those on

5.3 Solving Trigonometric Equations has the solutions and in the interval . Remember that since has a period of , there are infinitely many other solutions that can be written as: and General solution

5.3 Solving Trigonometric Equations The equation has infinitely many solutions. Any angles that are coterminal with are also solutions to the equation.

5.3 Solving Trigonometric Equations Solve: Add 1 to each side Divide each side by 3 Take the square root of both sides

5.3 Solving Trigonometric Equations You Try: Solve:

5.3 Solving Trigonometric Equations Find a general solution: Set each factor equal to 0

Find all solutions in the interval : 5.3 Solving Trigonometric Equations You Try: Find all solutions in the interval :

5.3 Solving Trigonometric Equations Solve: 2 sin2x + 3 cos x – 3 = 0

5.3 Solving Trigonometric Equations You Try: Solve: 2 sin2x = 2 + cosx on the interval [0,2π).

Using Inverse Functions Find all solutions of sec2x - 2 tan x = 4

Exit Ticket Solve cos2x – cosx = 2 on the interval [0,2π).

Homework Day 1: 5.3 pg. 364, 7-29 odd