5.3 solving trigonometric equations

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

ReviewSine

domain = all real numbers

range = [-1, 1]

period = 2p

y coordinate

Cosinedomain = all real numbers

range = [-1, 1]

period = 2p

x coordinate

Tangentdomain = x ≠p/2 + np

range = all real numbers

period = p

y/x

Solving Trig Equations

2sinx – 1 = 0 *Solve for sinx first

Where does sinx = ½ ? Remember sine is the y value

sinx = ½ on the unit circle

Collecting Like Terms

sinx + √2 = -sinx in the interval [0, 2p)

Extracting Square Roots

3tan2x – 1 = 0

Factoring-GCFcotxcos2x = 2cotx

Factoring – Quadratic Form

2sin2x – sinx – 1 = 0 in the interval [0, 2p)

Rewriting with a Single Trig FUNction2sin2x + 3cosx – 3 = 0

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)