Question

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

Answer 1

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)`