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Compute sin⁡(α−β)\sin ( \alpha - \beta ) And cos⁡(α−β)\cos ( \alpha - \beta )

Question 13

Multiple Choice

Compute sin⁡(α−β) \sin ( \alpha - \beta ) and cos⁡(α−β) \cos ( \alpha - \beta ) using the data below. sin⁡α=1213 where π2<α<π\sin \alpha = \frac { 12 } { 13 } \quad \text { where } \frac { \pi } { 2 } < \alpha < \pi cos⁡β=−1517 where π<β<3π2\cos \beta = - \frac { 15 } { 17 } \quad \text { where } \pi < \beta < \frac { 3 \pi } { 2 }


A) sin⁡(α−β) =140221\sin ( \alpha - \beta ) = \frac { 140 } { 221 } cos⁡(α−β) =−171221\cos ( \alpha - \beta ) = - \frac { 171 } { 221 }
B) sin⁡(α−β) =−220221\sin ( \alpha - \beta ) = - \frac { 220 } { 221 } cos⁡(α−β) =−21221\cos ( \alpha - \beta ) = - \frac { 21 } { 221 }
C) sin⁡(α−β) =−171221\sin ( \alpha - \beta ) = - \frac { 171 } { 221 } cos⁡(α−β) =140221\cos ( \alpha - \beta ) = \frac { 140 } { 221 }
D) sin⁡(α−β) =220221\sin ( \alpha - \beta ) = \frac { 220 } { 221 } cos⁡(α−β) =−21221\cos ( \alpha - \beta ) = - \frac { 21 } { 221 }
E) sin⁡(α−β) =−21221\sin ( \alpha - \beta ) = - \frac { 21 } { 221 } cos⁡(α−β) =−220221\cos ( \alpha - \beta ) = - \frac { 220 } { 221 }

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