Question

Find the exact values of sin (-pi/12)

Answer 1

`- 0.25881904`

Explanation:

Use the identity

`\sin( - x) = - \sin(x)`

so

`\sin( - (\pi)/(12) ) = - \sin( (\pi)/(12) )`

Use angle subtraction trig formula

`\sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y)`

In order to get pi/12, we can subtract

pi/4 and pi/6.

`\sin( (\pi)/(4) - (\pi)/(6) ) = \sin( (\pi)/(4) ) \cos( (\pi)/(6) ) - \cos( (\pi)/(4) ) \sin( (\pi)/(6) )`

Simplify.

`(( √(2) )/(2) * ( √(3) )/(2)) - ( ( √(2) )/(2) * (1)/(2) )`

`( √(6) )/(4) - ( √(2) )/(4)`

`( √(6) - √(2) )/(4)`

which is about

`0.25881904`

Remeber our sin is negative so our answer is

`- 0.25881904`

Answer 2

I showed the solution and the answer on a piece of paper in the photo