How do you simplify the expression #Sin(Arctan 3)#?

Question

6562 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-20T14:47:18

#sin(arctan(3))=3/sqrt(1+3^2)#

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

#sin(arctan(3))=3/sqrt(1+3^2)#

Answer 2 · 2017-02-20T14:54:36

#sin(arctan3)=3/sqrt10#

Let #arctan3=x#

and therefore #tanx=3#

This leads to #secx=sqrt(1+tan^2x)=sqrt(1+3^2)=sqrt10#

and #cosx=1/sqrt10#

#:.# #sin(arctan3)=sinx=sinx/cosx xx cosx#

= #tanx xxcosx=3xx1/sqrt10#

i.e. #sin(arctan3)=3/sqrt10#