How do you simplify #Cos( arcsin (x/3))#?

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Answer 1 · 2016-07-28T13:53:32

#sqrt(1-x^2/9)#

Let #a = arc sin (x/3)# is in Q1 or Q4..

Then,# sin a = x/3 and cos a = sqrt(1-x^2/9) >= 0#, in Q1 and Q4.

The given expression is cos a.

Answer 2 · 2016-07-28T14:04:37

#cos[arcsin(x/3)]=sqrt(9-x^2)/3" "->" "sqrt(1-x^2/9)#

#arcsin(x/3)# returns the angle #theta#

Tony B
#=>cos(theta)= sqrt(9-x^2)/3#

#=>cos(arcsin(x/3))=sqrt(9-x^2)/3#