What is $\frac{5 sin θ}{2}$ $(5sintheta)/2$ in terms of $cot θ$ $cottheta$ ?

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What is $\frac{5 sin θ}{2}$ $(5sintheta)/2$ in terms of $cot θ$ $cottheta$ ?

1 Answer

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Answer 1 · 2015-12-11T05:45:12

Write $(\frac{5}{2}) sin x$ $(5/2)sin x$ in terms of cot x.

Explanation:

Use the trig identity: ${sin}^{2} x = \frac{1}{1 + {cos}^{2} x}$ $sin^2 x = 1/(1 + cos^2 x)$
$sin x = {(\frac{1}{1 + cot x})}^{\frac{1}{2}}$ $sin x = (1/(1 + cot x))^(1/2)$
$(\frac{5}{2}) sin x = (\frac{5}{2}) {(\frac{1}{1 + {cot}^{2} x})}^{\frac{1}{2}} = {[\frac{25}{4 (1 + {cot}^{2} x)}]}^{\frac{1}{2}}$ $(5/2)sin x = (5/2)(1/(1 + cot^2 x))^(1/2) = [25/(4(1 + cot^2 x))]^(1/2)$

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What is $\frac{5 sin θ}{2}$ $(5sintheta)/2$ in terms of $cot θ$ $cottheta$ ?

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What is $\frac{5 sin θ}{2}$ $(5sintheta)/2$ in terms of $cot θ$ $cottheta$ ?