How do you find the exact value of sin((3pi)/4+(5pi)/6)?

1 Answer

-(sqrt6+sqrt2)/4

Explanation:

You could apply the formula:

sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta

Then:

sin(3/4pi+5/6pi)=sin(3/4pi)cos(5/6pi)+cos(3/4pi)sin(5/6pi)

=sqrt2/2(-1/2)+(-sqrt2)/2xxsqrt3/2

=-sqrt(2)/4-sqrt(6)/4

-(sqrt6+sqrt2)/4