Question

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

Answer 1

#( (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`