How do you evaluate sin ((7pi)/12)?

1 Answer
Jul 27, 2016

( (sqrt(2)+sqrt(6))/4)

Explanation:

sin(7pi/12)=sin(pi/4+pi/3)
Use the formula sin (a+b)=sina cosb+cosasinb
sin(pi/4+pi/3)=sin(pi/4)cos(pi/3)+cos(pi/4)sin(pi/3).....> 1
sin(pi/4)=sqrt(2)/2;cos (pi/4)=sqrt2/2
sin(pi/3)=sqrt(3)/2;cos(pi/3)=1/2
Plug these values on equation 1

sin(pi/4+pi/3)=(sqrt(2)/2)(1/2)+(sqrt(2)/2)*(sqrt(3)/2)

sin(pi/4+pi/3)=(sqrt(2)+sqrt(6))/4