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Published byAustin Booth Modified over 7 years ago

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Sum and Difference Formulas New Identities

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Cosine Formulas

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Sine Formulas

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Tangent Formulas

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Using Sum Formulas to Find Exact Values Find the exact value of cos 75 o Find the exact value of cos 75 o cos 75 o = cos (30 o + 45 o ) cos 75 o = cos (30 o + 45 o ) cos 30 o cos 45 o – sin 30 o sin 45 o cos 30 o cos 45 o – sin 30 o sin 45 o

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Find the Exact Value Find the exact value of Find the exact value of

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Exact Value Find the exact value of tan 195 o Find the exact value of tan 195 o

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Using Difference Formula to Find Exact Values Find the exact value of Find the exact value of sin 80 o cos 20 o – sin 20 o cos 80 o sin 80 o cos 20 o – sin 20 o cos 80 o This is the sin difference identity so... This is the sin difference identity so... sin(80 o – 20 o ) = sin (60 o ) = sin(80 o – 20 o ) = sin (60 o ) =

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Using Difference Formula to Find Exact Values Find the exact value of Find the exact value of cos 70 o cos 20 o – sin 70 o sin 20 o cos 70 o cos 20 o – sin 70 o sin 20 o This is just the cos difference formula This is just the cos difference formula cos (70 o + 20 o ) = cos (90 o ) = 0 cos (70 o + 20 o ) = cos (90 o ) = 0

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Finding Exact Values

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Establishing an Identity Establish the identity: Establish the identity:

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Establishing an Identity Establish the identity Establish the identity cos ( cos ( – cos cos cos ( cos ( – cos cos

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Solution cos cos – sin sin + cos cos sin sin cos cos – sin sin + cos cos sin sin cos cos cos cos cos cos cos cos cos cos cos cos cos cos = cos cos cos cos = cos cos

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Establishing an Identity Prove the identity: Prove the identity: tan ( = tan tan ( = tan

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Solution

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Establishing an Identity Prove the identity: Prove the identity:

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Solution

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Finding Exact Values Involving Inverse Trig Functions Find the exact value of: Find the exact value of:

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Solution Think of this equation as the cos ( Remember that the answer to an inverse trig question is an angle). Think of this equation as the cos ( Remember that the answer to an inverse trig question is an angle). So... is in the 1 st quadrant and is in the 4 th quadrant (remember range) So... is in the 1 st quadrant and is in the 4 th quadrant (remember range)

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Solution

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Solution

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Writing a Trig Expression as an Algebraic Expression Write sin (sin -1 u + cos -1 v) as an algebraic expression containing u and v (without any trigonometric functions) Write sin (sin -1 u + cos -1 v) as an algebraic expression containing u and v (without any trigonometric functions) Again, remember that this is just a sum formula Again, remember that this is just a sum formula sin ( = sin cos + sin cos sin ( = sin cos + sin cos

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Solution Let sin -1 u = and cos -1 v = Let sin -1 u = and cos -1 v = Then sin u and cos = v Then sin u and cos = v

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