Question

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

Answer 1

Answer:

$- 0.25881904$

Step-by-step explanation:

Use the identity

$\sin( - x) = - \sin(x)$

so

$\sin( - \frac{\pi}{12} ) = - \sin( \frac{\pi}{12} )$

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.

$\sin( \frac{\pi}{4} - \frac{\pi}{6} ) = \sin( \frac{\pi}{4} ) \cos( \frac{\pi}{6} ) - \cos( \frac{\pi}{4} ) \sin( \frac{\pi}{6} )$

Simplify.

$(\frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2}) - ( \frac{ \sqrt{2} }{2} \times \frac{1}{2} )$

$\frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4}$

$\frac{ \sqrt{6} - \sqrt{2} }{4}$

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