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

User Christian Gruber
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1 Answer

19 votes
19 votes

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}

User Fred Laurent
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