If $cot theta = - 2$ and $cos theta < 0$ , how do you find $sintheta$ ?

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Answer 1 · 2018-03-30T21:28:08

Start with the identity:

$1+ cot^2(theta)=csc^2(theta)$

Substitute $cot^2(theta) = (-2)^2$ :

$1+ (-2)^2=csc^2(theta)$

$5 = csc^2(theta)$

Substitute $csc^2(theta) = 1/sin^2(theta)$

$5 = 1/sin^2(theta)$

$sin^2(theta) = 1/5$

$sin(theta) = +-sqrt5/5$

Because we are told that $cos(theta) < 0$ and $cot(theta) = -2$ , we know that the sine function must be positive in this quadrant:

$sin(theta) = sqrt5/5$

If cot theta = - 2cot theta = - 2 and cos theta < 0cos theta < 0, how do you find sinthetasintheta?