Question

The angle t is an acute angle and sint is given. Use the Pythagorean identity sin’t+ cos?t= 1 to find costsint =6

Answer 1

we have

`\sin (t)=\frac{\sqrt[]{5}}{6}`

Remember that

`\sin ^2(t)+\cos ^2(t)=1`

substitute the given value

`(\frac{\sqrt[]{5}}{6})^2+\cos ^2(t)=1`
`\begin{gathered} (5)/(36)+\cos ^2(t)=1 \\ \cos ^2(t)=1-(5)/(36) \\ \cos ^2(t)=(31)/(36) \\ cos(t)=\pm\frac{\sqrt[]{31}}{6} \end{gathered}`

the angle t is an acute angle and the sine is positive, that means, the angle t lies in the first quadrant

so

the cosine is positive

therefore

`cos(t)=\frac{\sqrt[]{31}}{6}`