How do you find the exact value of $cos(arctan (5/2))$ ?

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Answer 1 · 2016-01-26T09:26:20

$cos (arctan(5/2))=(2sqrt29)/29$

Let $A$ be an angle whose tangent $=5/2$

Let $A=arctan(5/2)$

Then $tan A=5/2$

Imagine a right triangle with opposite side $a=5$ and adjacent side $b=2$ . Compute hypotenuse $c$

$c=sqrt(a^2+b^2)$

$c=sqrt(5^2+2^2)$

$c=sqrt29$

Then, the cosine function of $A$

$cos A=b/c=2/sqrt29=(2sqrt29)/29$

Have a nice day !!! From the Philippines...

How do you find the exact value of cos(arctan (5/2))cos(arctan (5/2))?