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} \frac{5}{36}+\cos ^2(t)=1 \\ \cos ^2(t)=1-\frac{5}{36} \\ \cos ^2(t)=\frac{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

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