Find sin θ if cot θ = - 4 and cos θ

Question

Find sin θ if cot θ = - 4 and cos θ < 0.

jhonyy9 · Answer

us cot x =cos x / sin x

anonymous · Answer

I have, and I understand that sin(x) must be positive. sin(x) must equal cos(x)/-4 right?

jhonyy9 · Answer

yes

anonymous · Answer

I don't know what to do next. The multiple choice answers are: -17, sqrt(17)/17, -1/4, and sqrt(17)/4

anonymous · Answer

anyone?

anonymous · Answer

$$\frac{ \cos \theta }{ \sin \theta } = -4$$$$\cos \theta = -4\sin \theta$$You can substitute that expression for cos in the following:$$\cos ^{2}\theta + \sin ^{2}\theta = 1$$

anonymous · Answer

$$\left( -4\sin \theta \right)^{2} + \sin ^{2}\theta = 1$$

anonymous · Answer

$$16\sin ^{2}\theta + \sin ^{2}\theta = 1$$From here, you should be able to simplify and get the answer.

anonymous · Answer

When simplifying, as a last step, rationalize your denominator.

anonymous · Answer

Also, bear in mind that the cotangent and cosine are negative.  Therefore, the sine is positive.

dumbcow · Answer

another approach is to use a right triangle 
cot = adj/opp
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the hypotenuse can be found using pythagorean thm

anonymous · Answer

Thanks guys!!! Really appreciate it.