8.4Sum&DiffFormulas

8.4Sum&DiffFormulas - 8.4 Sum and Difference...

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Unformatted text preview: 8.4 Sum and Difference Formulas [1] cos(α + β ) = cosα cosβ ­ sinα sinβ [3] sin(α + β ) = sinα cosβ + cosα sinβ tanα + tan β [5] tan(α + β) = 1 ­ tanαtan β π Identities: [7] cos - θ = sin θ 2 [2] cos(α ­ β ) = cosα cosβ + sinα sinβ [4]sin(α ­ β ) = sinα cosβ ­ cosα sinβ tanα ­ tan β [6] tan(α ­ β) = 1 + tanαtan β π [8] sin - θ = cosθ 2 One use of the sum and difference formulas is to obtain the exact value of the sine, cosine, or tangent for angles that can be expressed as the sum or difference of known angles. Find the exact value of each trigonometric function: ( 1. cos 285 o ) 13π 12 2. sin 5π 3. tan − 12 17π 12 4. csc Find the exact value of each expression: 5. cos20°cos80° + sin 20°sin80° 6. sin 4π 7π 4π 7π cos −cos sin 18 18 18 18 Find the exact value of each of the following under the given conditions: 5 3π 1 π 7. Find sin(α ­ β ) if tanα = 12 , π < α < 2 ; sin β = − 2 , − 2 < β < 0 8. If cos θ = ¼ , θ in quadrant IV, find: π cos θ + 6 Find the exact value of each expression: 3 −1 −1 9. sin sin 2 + cos 1 XTRA E PRACTICE 8.3 Establish each identity: 1. sin θ ( cot θ + tan θ ) = sec θ sin θ 1+ cos θ 2. csc θ − cot θ = 3. sin2 θ − tan θ = tan2 θ cos 2 θ − cot θ 8.4 Find the exact value using Sum & Difference formulas: 19π 4. tan 12 5. tan 40o − tan 10o 1+ tan 40o tan 10o o 6. cos(α + β) if cos α = 7. 5 π 4π , 0 < α < ; sin β = − , − < β < 0 5 2 5 2 5 3 cos tan−1 ÷− sin −1 − ÷ 12 5 ...
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This note was uploaded on 01/04/2012 for the course MAC 1114 taught by Professor Patriciabishop during the Fall '11 term at Miami Dade College, Miami.

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8.4Sum&amp;DiffFormulas - 8.4 Sum and Difference...

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