Mathematics: Ineed 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?

Ineed the answer asap and i m aweful at this kind

Ответ:

imgoingtowriteabook

13.03.2022

You have that $\cos \theta=- \frac{2}{5}$ and $\tan \theta\ \textgreater \ 0$ . Since $\tan \theta= \frac{\sin\theta}{\cos\theta}$ 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 $\sqrt{5^2-2^2} = \sqrt{21}$ . Then $\sin\theta=- \frac{ \sqrt{21} }{5}$ .