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6.2 Cofunction and Double-Angle Identities Fri Dec 5 Do Now Simplify (sinx + cosx)(sinx – cosx)
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Cofunction Identities
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Proof These can be proven using the sum and difference identities Proof of sin identity:
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Cofunction Identities for Sine and Cosine Because of sine and cosine’s relationship, they have 2 more identities
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Finding other identities Ex: Find an identity for
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Ex2 Find an identity for
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Double Angle Identities Double-Angle identities give trig function values of 2x These are also proven using the sum identities
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Ex Given tanx = -3/4, and x is in quadrant 2, find 1) sin2x 2) cos2x 3) tan2x 4) The quadrant 2x lies in
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Ex Find equivalent expressions for sin 3x in terms of x
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Ex Find equivalent expressions of (cosx)^3 in terms of x or 2x, raised only to the first power
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Closure Find an exact value of sin2x, cos2x, and tan2x if cosx = 5/13 in quadrant 1 HW: p.553 #3-15, 23, 29 33
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6.2 Half Angle Identities Mon Dec 8 Do Now Find the exact value of sin2x cos2x and tan2x if tanx = -15/8 in quadrant 2
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HW Review: p.553 #3-15, 23, 29 33
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Half-Angle Identities We can find trig functions of angles that are half of what we already know how to find
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Ex1 Find the exact value of
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Ex2 Simplify
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Ex3 Simplify
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Closure Given sinx = 4/5, evaluate sin (x/2) HW: p.554 #17-21 25 27 31
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