What is # cos (Arcsin (3/5))#?

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Answer 1 · 2015-07-21T22:45:58

#4/5#

First consider that : #theta=arcsin(3/5)#

#theta# just represents an angle.

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

If #theta=arcsin(3/5)# then,

#=>sin(theta)=3/5#

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

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

#=>cos(theta)=sqrt(1-(3/5)^2)=sqrt((25-9)/25)=sqrt(16/25)=color(blue)(4/5)#