What is #sin(arccos(5/13))#?

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Answer 1 · 2015-07-21T22:29:39

#12/13#

First consider that : #theta=arccos(5/13)#

#theta# just represents an angle.

This means that we are looking for #color(red)sin(theta)!#

If #theta=arccos(5/13)# then,

#=>cos(theta)=5/13#

To find #sin(theta)# We use the identity : #sin^2(theta)=1-cos^2(theta)#

#=>sin(theta)=sqrt(1-cos^2(theta)#

#=>sin(theta)=sqrt(1-(5/13)^2)=sqrt((169-25)/169)=sqrt(144/169)=color(blue)(12/13)#