5.3 solving trigonometric equations *use standard algebraic techniques to solve trig equations...
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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)