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Given that the cos θ -5/13 and θ is in quadrant 4, what’s the value of sin θ?

1 Answer

4 votes

we have that

cos θ= 5/13 -----> given

θ is in quadrant 4 ----> that means

the value of the sine is negative and the value of cosine is positive

Remember that


\sin ^2\theta+\cos ^2\theta=1

substitute given value


\sin ^2\theta+((5)/(13))^2=1
\begin{gathered} \sin ^2\theta=1-(25)/(169) \\ \end{gathered}
\sin ^2\theta=(144)/(169)
\sin ^{}\theta=-(12)/(13)

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