Using sum or difference formulas Find the exact value of sin

Using sum or difference formulas, Find the exact value of sin(345 degree). Express your answer in the form sin(345 degree)=squareroot a(1-squareroot b/4 for some numbers a and b.

Solution

sin(345⁰)

=sin(300^o+45⁰)

sin(A+B)=sinAcosB +cosAsinB

=sin(300^o)cos(45⁰) +cos(300^o)sin(45⁰)

=sin(360^o-60^o)cos(45⁰) +cos(360^o-60⁰)sin(45⁰)

=-sin(60^o)cos(45⁰) +cos(60⁰)sin(45⁰)

=-(3 /2)(1/2) +(1/2)(1/ 2)

=(1 -3)/(22)

=2(1-3)/(2 *22)

=2(1-3)/4

a=2

b=3