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Published byBernard Eugene Norton Modified over 9 years ago

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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

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

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

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sinx = ½ on the unit circle

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

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Extracting Square Roots 3tan 2 x – 1 = 0

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Factoring-GCF cotxcos 2 x = 2cotx

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Factoring – Quadratic Form 2sin 2 x – sinx – 1 = 0 in the interval [0, 2 )

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Rewriting with a Single Trig FUNction 2sin 2 x + 3cosx – 3 = 0

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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, 2 )

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