How do you use $csc θ = 4$ $csctheta=4$ to find $sec θ$ $sectheta$ ?

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How do you use $csc θ = 4$ $csctheta=4$ to find $sec θ$ $sectheta$ ?

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Answer 1 · 2017-02-04T06:38:22

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

Explanation:

As $csc θ = 4$ $csctheta=4$ , $sin θ = \frac{1}{csc θ} = \frac{1}{4}$ $sintheta=1/csctheta=1/4$

and $cos θ = \sqrt{1 - {sin}^{2} θ} = \sqrt{1 - {(\frac{1}{4})}^{2}} = \sqrt{\frac{15}{16}} = \pm \frac{\sqrt{15}}{4}$ $costheta=sqrt(1-sin^2theta)=sqrt(1-(1/4)^2)=sqrt(15/16)=+-sqrt15/4$

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

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How do you use $csc θ = 4$ $csctheta=4$ to find $sec θ$ $sectheta$ ?

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How do you use cscθ=4csctheta=4 to find secθsectheta?

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How do you use $csc θ = 4$ $csctheta=4$ to find $sec θ$ $sectheta$ ?