Given $\sin \theta = - \frac { 1 } { 4 }$ and an...

Question

$Given $\sin \theta = - \frac { 1 } { 4 }$ and an...$

Given $\sin \theta = - \frac { 1 } { 4 }$ and angle $\theta$ is in Quadrant III, what is the exact value of $\cos \theta$ in simplest form? Simplify all radicals if needed.

Answer: $\cos \theta = $

Answer

$\sin \theta = - \frac { 1 } { 4 } $

$ \sin ^ { 2 } \theta + \cos ^ { 2 } \theta = 1 $

$ \cos \theta = \pm \sqrt { 1 - ( - \frac { 1 } { 4 } ) ^ { 2 } } $

$ \theta i s \operatorname { in } \theta \frac { \pi } { 11 } $

$ \therefore \cos \theta < 0 $

$ \therefore \cos \theta = - \sqrt { \frac { 15 } { 16 } } = - \frac { \sqrt { 15 } } { 4 }$

Solution

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