5.3 Solving Trigonometric Equations Day 2 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.

Solve: 5.3 Solving Trigonometric Equations Day 2

Precalculus5.3 Solving Trigonometric Equations 3 Find all solutions in the interval [0,2π) cosx + 1 = sinx Solution: x = π, x = π/2 When squaring and converting to a quadratic you must plug your solutions back into the original equation to make sure that all solutions work!!!! 3π/2 is extraneous (a number obtained in solving an equation that is NOT a solution) 5.3 Solving Trigonometric Equations Day 2

5.3 Solving Trigonometric Equations You Try Find all solutions of 1 + sin x = cos x General solution: x = 2nπ, x = 3π/2 + 2nπ

5.3 Functions Involving Multiple Angles Solve: 2cos3t–1 = 0 on the interval [0,2π)

5.3 Functions Involving Multiple Angles Solve: 2cos3t–1 = 0. General solution:

5.3 Functions Involving Multiple Angles Find the general solution of:

5.3 Solving Trigonometric Equations You Try Solve:

Approximating Solutions Approximate the solutions of x = 2 sin x in the interval [-π,π]

Techniques for Solving Trig Equations 1.Collecting Like Terms 2.Extracting Square Roots 3.Factoring 4.Rewriting with a Single Trig Function 5.Converting to Quadratic Type 6.Solve for Multiple Angles 7.Using Inverse Functions 8.Approximating Solutions

Homework 5.3 pg 364: 31-53odd, odd