Compute $\cos ( \alpha + \theta )$ And $\cos ( \alpha - \theta )$

question 8

Multiple Choice

Compute $\cos ( \alpha + \theta )$ and $\cos ( \alpha - \theta )$ using the data below. $\sin \alpha = \frac { 3 } { 5 } \quad \text { where } \frac { \pi } { 2 } < \alpha < \pi$ $\cos \theta = \frac { 5 } { 13 } \quad \text { where } - 2 \pi < \theta < - \frac { 3 \pi } { 2 }$

• A) \(\cos ( \alpha + \theta ) = \frac { 21 } { 221 }\) \(\cos ( \alpha - \theta ) = - \frac { 171 } { 221 }\)
• B) \(\cos ( \alpha + \theta ) = - \frac { 56 } { 65 } \cos ( \alpha - \theta ) = \frac { 16 } { 65 }\)
• C) \(\cos ( \alpha + \theta ) = \frac { 16 } { 65 }\) \(\cos ( \alpha - \theta ) = - \frac { 56 } { 65 }\)
• D) \(\cos ( \alpha + \theta ) = \frac { 56 } { 65 }\) \(\cos ( \alpha - \theta ) = \frac { 16 } { 65 }\)
• E) \(\cos ( \alpha + \theta ) = - \frac { 171 } { 221 }\) \(\cos ( \alpha - \theta ) = \frac { 21 } { 221 }\)

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