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mathematics

Using fundamental identities to find the value of the trigonometric function, find the sin theta if cos = -square root of 11/6 and theta is in quadrant III

I assume you meant $\cos \theta = -\sqrt{11/16}$ not $-sqrt{11/6}$ .

Given:

$ \cos \theta = - \sqrt {11/16} $

Use the fundamental identity

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

Rearrange to get sin as a function of cosine:

$ \sin \theta = \sqrt {1 - \cos^2 \theta} $

For this problem you know the value of $\cos \theta$ , so plug and chug. Use the fact that $\theta$ is in the 3rd quadrant to determine the correct sign for $\sin \theta$ .

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