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Trigonometry
Question

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: $$\cos \theta =$$

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

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

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

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

$$\therefore \cos \theta < 0$$

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

Solution
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