5.3 Solving Trigonometric Equations

1. 5.3 Solving Trigonometric Equations *use standard algebraic techniques to solve trig equations *solve trig equations in quadratic form *solve trig equations with multiple angles *use inverse trig functions to solve trig equations

2. Review • Sine • domain = all real numbers • range = [-1, 1] • period = 2p • y coordinate • Cosine • domain = all real numbers • range = [-1, 1] • period = 2p • x coordinate • Tangent • domain = x ≠p/2 + np • range = all real numbers • period = p • y/x

3. Solving Trig Equations • 2sinx – 1 = 0*Solve for sinx first • Where does sinx = ½ ? Remember sine is the y value

4. sinx = ½ on the unit circle

5. Collecting Like Terms • sinx + √2 = -sinx in the interval [0, 2p)

6. Extracting Square Roots • 3tan2x – 1 = 0

7. Factoring-GCF • cotxcos2x = 2cotx

8. Factoring – Quadratic Form • 2sin2x – sinx – 1 = 0 in the interval [0, 2p)

9. Rewriting with a Single Trig FUNction • 2sin2x + 3cosx – 3 = 0

10. Squaring Both Sides • Sometimes when you square both sides of an equations to obtain a quadratic you get extraneous solutions. Be sure to check your solutions!! • cosx + 1 = sinx in the interval [0, 2p)