What is $(sintheta)/4$ in terms of $sectheta$ ?

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Answer 1 · 2016-02-09T03:18:34

$sqrt(sec^2theta-1)/(4sectheta)$

First, we should write $sintheta/4$ in terms of $costheta$ . Then, since $sectheta=1/costheta$ , it's a simple fix to switch from one to the other.

We should make use of the Pythagorean identity:

$sin^2theta+cos^2theta=1" "=>" "sin^2theta=1-cos^2theta" "=>" "sintheta=sqrt(1-cos^2theta)$

Thus,

$sintheta/4=sqrt(1-cos^2theta)/4=sqrt(1-1/sec^2theta)/4$

Although this does meet the parameters of the question, we can algebra our way to a prettier looking answer.

$sintheta/4=sqrt((sec^2theta-1)/sec^2theta)/4=sqrt(sec^2theta-1)/(4sectheta)$

What is (sintheta)/4(sintheta)/4 in terms of secthetasectheta?