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Find cos0 if sin 0 =-1/3 and tan0>0

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The Solution:

Given:


\begin{gathered} \sin\theta=-(1)/(3) \\ \\ \tan\theta>0 \end{gathered}

We are asked to find the value of:


\cos\theta

So,


\begin{gathered} \sin\theta=-(1)/(3) \\ \\ Taking\text{ the }\sin^(-1)\text{ of both sides, we get:} \end{gathered}
\theta=\sin^(-1)(-(1)/(3))=-19.47^o

Note:

Sins of angles is only negative in the 3rd and 4th quadrants.

Since, it is given that:


\tan\theta>0\text{ \lparen positive\rparen}

Thus, it follows that the angle of concern falls into the 3rd quadrant.

User Sophia Price
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