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**Peleus** If $\displaystyle \sin\theta = \frac{1}{3}$ and $\displaystyle \tan\theta < 0 $ then what is $\displaystyle \cos\theta$

Like I said I feel completely dumb here. I know this is so basic I'm just having a mental block with it.

Multiple choice answers are

a) $\displaystyle \frac{1}{3}$

b) $\displaystyle \frac{-3}{\sqrt{10}}$

c) $\displaystyle \frac{-1}{2\sqrt{2}}$

d) $\displaystyle \frac{-2\sqrt{2}}{3}$

e) $\displaystyle \frac{1}{\sqrt{10}}$

Because of the nature of the answers I know I'd have to use the unit triangle somewhere. Because tan is negative and sin is positive the answer is in quadrent 2. In other words sin1/3 = 180 - cos.

What I don't know though is how we've got the unit triangle to give sin 1/3, my stupid question is how do I get sin 1/3 on the unit triangle?