Question

If \cos\left(\frac{\pi}{10}\right) = \sin(\theta) and $0 < \theta < \frac{\pi}{2}$, then \begin{equation*}\theta = \underline{\qquad} radians\end{equation*}

          If \cos\left(\frac{\pi}{10}\right) = \sin(\theta) and $0 < \theta < \frac{\pi}{2}$, then \begin{equation*}\theta = \underline{\qquad} radians\end{equation*}
        
If cos((π)/(10)) = sin(θ) and 0 < θ < (π)/(2), then 
    θ =      radians

Added by Mary D.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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If cos((pi )/(10))=sin( heta ) and 0< heta <(pi )/(2), then heta = radians TT TT = sin(0) and 0 < 0 < then 2 If cos 10 =0 radians
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Transcript

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00:01 We have given we have given theta equal to sine theta given sine theta equal to tib by 5 and theta is from 0 to pi by 2 0 it means theta lies in the first quadrant cos and sine all are positive here so we have cost theta by 2 so it will be equal to using the half angle formula so 1 plus cost theta divided by 2 to the whole square root so now we we will calculate the cost theta separately so cost theta equal to 1 minus sine square theta under root so as it is in the first quadrant so our value is positive so we know that sine theta is 3 by 5 we will put here and calculate the value of cost theta 1 minus sine square theta is 3 by 5 whole square so it will be 9 by 25 so it would give us 25 minus 9 divided by 25 square root so 16 divided by 25 square root so it would be equal to equal to 4 by 5 5 so we know that cost theta equal to 4 by 5.
02:19 So we will put it here now again...
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