Use a double angle formula to determine the exact value of sin ( −13π / 12 )

Answer 1

You can’t use a double-angle formula here (since - 13π/12 isn’t twice any angle whose trig values we know offhand), but we can use the difference formula for sinx. We need to find two “friendly” angles whose difference is - 13π/12, so π/4 and 4π/3 will suit our needs well.

sin(-13π/12) = sin(π/4 - 4π/3)

Now we use the difference formula: sin(π/4 - 4π/3) = sin(π/4)⋅cos(4π/3) - sin(4π/3)⋅cos(π/4)

= (√2/2)⋅(- 1/2) - (√3/2)⋅(√2/2) = - √2/4 - √6/4

Answer 2

I would not use a double angle formula. Rather a sum formula would work

sin (-13πο/ 12)

-sin(13π / 12)

-sin (4π/12 + 9π/12)

-sin (π/3 + 3π/4)

-[sin π/3 cos 3π/4 + cos π/3 sin 3π/4]

Can you complete?