How do you simplify the expression #sin(arctan x)#?

1 Answer
Leland Adriano Alejandro
Jul 31, 2016

#sin(arctan x)=x/(+-sqrt(x^2+1))#

Explanation:

The solution:

#arctan x# is an angle whose tangent function #=x/1#

Considering the sides of the right triangle. We have opposite side #=x#, adjacent side #=1# and hypotenuse #=sqrt(x^2+1)#

Therefore the sine of this angle #=("opposite side")/("hypotenuse")=x/sqrt(x^2+1)#

God bless....I hope the explanation is useful.

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