Compute $\sin ( \alpha - \beta )$ And $\cos ( \alpha - \beta )$

question 13

Multiple Choice

Compute $\sin ( \alpha - \beta )$ and $\cos ( \alpha - \beta )$ using the data below. $\sin \alpha = \frac { 12 } { 13 } \quad \text { where } \frac { \pi } { 2 } < \alpha < \pi$ $$\cos \beta = - \frac { 15 } { 17 } \quad \text { where } \pi < \beta < \frac { 3 \pi } { 2 }$$

• A) \(\sin ( \alpha - \beta ) = \frac { 140 } { 221 }\) \(\cos ( \alpha - \beta ) = - \frac { 171 } { 221 }\)
• B) \(\sin ( \alpha - \beta ) = - \frac { 220 } { 221 }\) \(\cos ( \alpha - \beta ) = - \frac { 21 } { 221 }\)
• C) \(\sin ( \alpha - \beta ) = - \frac { 171 } { 221 }\) \(\cos ( \alpha - \beta ) = \frac { 140 } { 221 }\)
• D) \(\sin ( \alpha - \beta ) = \frac { 220 } { 221 }\) \(\cos ( \alpha - \beta ) = - \frac { 21 } { 221 }\)
• E) \(\sin ( \alpha - \beta ) = - \frac { 21 } { 221 }\) \(\cos ( \alpha - \beta ) = - \frac { 220 } { 221 }\)

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