Question

Please help!!! I need the answer asap and I'm aweful at this kind of Math.

If cos theta=-2/5 and tan theta>0, what is the value of sin theta?

Answer 1

You have that
`\cos \theta=- (2)/(5)` and
`\tan \theta\ \textgreater \ 0`. Since
`\tan \theta= (\sin\theta)/(\cos\theta)` you can conclude that
`\sin\theta\ \textless \ 0`.
Let consider the right triangle with leg 2, hypotenuse 5 and an angle
`\theta`, which lies between given leg and hypotenuse. Be Pythagorean theorem the second leg is equal to
`√(5^2-2^2) = √(21)`. Then
`\sin\theta=- ( √(21) )/(5)`.