What does $cos (arctan (\frac{- 3 π}{4}))$ $cos(arctan((-3pi)/4))$ equal?

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What does $cos (arctan (\frac{- 3 π}{4}))$ $cos(arctan((-3pi)/4))$ equal?

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Answer 1 · 2016-01-25T08:00:39

$cos (arctan (\frac{- 3 π}{4})) = \frac{4}{\sqrt{16 + 9 π^{2}}}$ $cos(arctan((-3pi)/4))=4/sqrt(16+9pi^2)$

Explanation:

We are looking for the cosine function of an angle A. The angle A whose tangent = $\frac{- 3 π}{4}$ $(-3pi)/4$

$A = arctan (\frac{- 3 π}{4})$ $A=arctan((-3pi)/4)$ it is an angle

Just imagine a right triangle with angle A with opposite side $= - 3 π$ $=-3pi$
and with adjacent side $= 4$ $=4$ . Then we have a hypotenuse $= \sqrt{4^{2} + {(- 3 π)}^{2}} = \sqrt{16 + 9 π^{2}}$ $=sqrt(4^2+(-3pi)^2)=sqrt(16+9pi^2)$

$cos A = \frac{4}{\sqrt{16 + 9 π^{2}}}$ $cos A=4/sqrt(16+9pi^2)$

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What does $cos (arctan (\frac{- 3 π}{4}))$ $cos(arctan((-3pi)/4))$ equal?

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Explanation:

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