Find the exact value of sin (theta) with cos(theta) = -3/4 and with its terminal side in quadrant iii. a. 4/3b. -7/4c. -(sqrt 7)/4d. (sqrt 7)/4

Actually, it does work out just fine with the values you have up there. If the cos of the angle is -3/4, and it is in the third quadrant, the value along the x axis is -3 and the hypotenuse is 4. Always positive. That means that we have to find the missing side using Pythagorean's Theorem.

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If the side opposite the reference angle is the square root of 7, it is also negative because in the third quadrant both x and y are negative, so the sin of that angle will be , choice c.

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