math
posted by TEETEE .
Use an Addition or Subtraction Formula to find the exact value of the expression.
Sin(−5π/12)

some students have less difficulty if the angle is in degrees.
Let's try this approach ....
5π/12 radians = 75°
so sin(5π/12)
= sin(75°) which is in quadrant IV, making the sine negative
= sin(75°)
= sin(30° + 45°)
= (sin30cos45 + cos30sin45)
= ( (1/2)(√2/2) + (√3/3)(√2/2) )
=  √2/4  √6/4
so sin(05π/12) = √2/4  √6/4
check:
on my calculator:
sin(5π/12) = .9659...
and √2/4  √6/4 = .9659..
My answer is correct