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mac1147_lecture21_1_b

mac1147_lecture21_1_b - L21 Sum and Difference Formulas...

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296 L21 Sum and Difference Formulas; Double-angle and Half-angle Formulas; Solving Right Triangles Sum and Difference Identities Caution : () cos cos cos α βα β ≠− for arbitrary angles and . Example : 3 cos 2 π 3 cos cos 2 Sum and Difference Formulas for Cosines : cos cos cos sin sin += cos cos cos sin sin −= + Example : Find the exact value of 5 cos 12 .

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297 Sum and Difference Formulas for Sines : () sin sin cos cos sin α βα β += + sin sin cos cos sin −= Example : Simplify: 3 sin 2 π θ ⎛⎞ ⎜⎟ ⎝⎠ Example : Find the exact value of 22 cos cos sin sin 51 0 5 1 0 ππ
298 Example : Given that 8 cos 17 s = − , s is in quadrant III, and 3 sin 5 t =− , t is in quadrant IV. Find: () sin s t +

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299 Example : Evaluate 11 12 8 cos sin ( ) cos ( ) 13 17 −− ⎛⎞ −+ ⎜⎟ ⎝⎠
300 Sum and Difference Formulas for Tangents : () tan tan tan 1t a n t a n α β αβ + += tan tan tan a n t a n −= + Example : Find the exact values of tan 105 ° tan80 tan 55 a n 8 0 t a n 5 5 °− − ° °

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301 Double-angle and Half-angle Formulas sin 2 θ= cos2 tan2
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mac1147_lecture21_1_b - L21 Sum and Difference Formulas...

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