How do you find the exact value of $cos(arctan(3/4))$ ?

Question

14396 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-28T18:15:55

$cosy=4/5$

Pose:

$y=arctan(3/4)$

this means that:

$tany=3/4$

Using the trigonometric identity $sec^2t=1+tan^2t$ :

$1/cos^2y = 1+tan^2y = 1+9/16=25/16$

or:

$cos^2y = 16/25$

and:

$cosy=4/5$

where we take the positive root, since $arctan(3/4)$ is in the interval $(0,pi/2)$

How do you find the exact value of cos(arctan(3/4))cos(arctan(3/4))?