How do you find the values of the six trigonometric functions given $csc θ = 4$ $csctheta=4$ and $cot θ < 0$ $cottheta<0$ ?

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How do you find the values of the six trigonometric functions given $csc θ = 4$ $csctheta=4$ and $cot θ < 0$ $cottheta<0$ ?

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Answer 1 · 2018-02-25T16:07:26

$sin θ = \frac{1}{4}$ $sintheta=1/4$ , $cos θ = - \frac{\sqrt{15}}{4}$ $costheta=-sqrt15/4$ , $tan θ = - \frac{1}{\sqrt{15}}$ $tantheta=-1/sqrt15$
$cot θ = - \sqrt{15}$ $cottheta=-sqrt15$ , $sec θ = - \frac{4}{\sqrt{15}}$ $sectheta=-4/sqrt15$ and $csc θ = 4$ $csctheta=4$ .

Explanation:

Let us consider the identity ${csc}^{2} θ = 1 + {cot}^{2} θ$ $csc^2theta=1+cot^2theta$

as $csc θ = 4$ $csctheta=4$ , we have $16 = 1 + {cot}^{2} θ$ $16=1+cot^2theta$ and

${cot}^{2} θ = 15$ $cot^2theta=15$ and as $cot θ < 0$ $cottheta<0$ , $cot θ = - \sqrt{15}$ $cottheta=-sqrt15$

Therefore $tan θ = - \frac{1}{\sqrt{15}}$ $tantheta=-1/sqrt15$ and $sin θ = \frac{1}{4}$ $sintheta=1/4$

As #tantheta=sintheta/costheta, this means

$cos θ = \frac{sin θ}{tan θ} = \frac{\frac{1}{4}}{- \frac{1}{\sqrt{15}}} = - \frac{\sqrt{15}}{4}$ $costheta=sintheta/tantheta=(1/4)/(-1/sqrt15)=-sqrt15/4$

and $sec θ = - \frac{4}{\sqrt{15}}$ $sectheta=-4/sqrt15$

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How do you find the values of the six trigonometric functions given $csc θ = 4$ $csctheta=4$ and $cot θ < 0$ $cottheta<0$ ?

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Explanation:

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Science

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How do you find the values of the six trigonometric functions given cscθ=4csctheta=4 and cotθ<0cottheta<0?

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Explanation:

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How do you find the values of the six trigonometric functions given $csc θ = 4$ $csctheta=4$ and $cot θ < 0$ $cottheta<0$ ?