What is $\frac{3 tan θ}{4}$ $(3tantheta)/4$ in terms of $cos θ$ $costheta$ ?

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What is $\frac{3 tan θ}{4}$ $(3tantheta)/4$ in terms of $cos θ$ $costheta$ ?

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Answer 1 · 2016-01-01T04:21:28

$= \frac{3}{4} \frac{\sqrt{1 - {cos}^{2} (θ)}}{cos (θ)}$ $=3/4 sqrt(1-cos^2(theta))/cos(theta)$

Explanation:

$\frac{3}{4} tan (θ)$ $3/4 tan(theta)$

Rewriting $tan (θ)$ $tan(theta)$ in terms of $\frac{sin (θ)}{cos (θ)}$ $sin(theta)/cos(theta)$
$= \frac{3}{4} \frac{sin (θ)}{cos (θ)}$ $=3/4 sin(theta)/cos(theta)$

Use the identity to change sine to cosine
${sin}^{2} (θ) = 1 - {cos}^{2} (θ)$ $sin^2(theta) = 1-cos^2(theta)$

$= \frac{3}{4} \frac{\sqrt{1 - {cos}^{2} (θ)}}{cos (θ)}$ $=3/4 sqrt(1-cos^2(theta))/cos(theta)$ Answer as needed.

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What is $\frac{3 tan θ}{4}$ $(3tantheta)/4$ in terms of $cos θ$ $costheta$ ?

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What is $\frac{3 tan θ}{4}$ $(3tantheta)/4$ in terms of $cos θ$ $costheta$ ?