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

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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)#