Solving Basic Trigonometric Equations Digital Lesson Section 5-3

Thursday: Announcements Tomorrow ends 3 weeks for Progress Reports Retest tomorrow morning 2

3 Objectives I can solve trig equations using algebra strategies I understand that equations have multiple answers

4 The Basics Trig equations have infinitely many solutions depending on the period of the function  for sine,cosine,secant, cosecant  for tangent, cotangent. 3.If we restrict the value of a function to 2 quadrants, a trig equation will have unique solutions. Trig equations can be solved by a mixture of algebraic and trigonometric techniques. 1.reducing, substitution, simplification, etc. 2. Like terms, factoring, square roots, quadratic formula

5 x y π π 6 -7 π 6 π 6 5 π 6 13 π 6 17 π 6 25 π 6 -π-π -2 π -3 π π 2π2π 3π3π 4π4π All the solutions for x can be expressed in the form of a general solution. x = is one of infinitely many solutions of y = sin x. π 6 x = + n2π and x = + n2 π (n = 0, ±1, ± 2, ± 3,  ). 6 π5π5π 6 sin x = is a trigonometric equation. y = y=sin x

6 Example 1

7 Example 2

8 Example 3

9 Homework WS 11-4