Question

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

Answer 1

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.