Question

use the sum/difference identities to evaluate exactly
sin pi/12

Answer 1

Hmm so we first want to rewrite `pi/12` in terms of `pi/6`'s, `pi/3`'s and `pi/4`'s maybe. If we have the angle written in terms of known special angles, we can apply a sum/difference identity to it and it shouldn't be too bad.

Answer 2

\[\Large\bf\frac{\pi}{12}\quad=\quad \frac{9\pi}{12}-\frac{8\pi}{12}\quad=\quad \frac{3\pi}{4}-\frac{2\pi}{3}\]Understand what I did there? :o

Answer 3

\[\Large\bf \sin\left(\color{#DD4747 }{\frac{\pi}{12}}\right)\quad=\quad \sin\left(\color{#DD4747 }{\frac{3\pi}{4}-\frac{2\pi}{3}}\right)\]

Answer 4

From there, you should be able to apply your `Difference Formula for Sine`.
Let me know if you're still confused.

Answer 5

i just lost

Answer 6

use the identity

sin(a - b) = sina cosb - cosa sinb

put a = 3pi/4 and b = 2pi/3

Answer 7

you can find the exact values sines and cosines of 3pi/4 and 2pi/3 from the following: