Question

How do you use the sum or difference identities to find the exact value of `sin735^circ`?

Answer 1

`sqrt(2 - sqrt3)/2`

Explanation:

sin 735 = sin (15 + 720) = sin (15 + 2(360)) = sin 15.
Evaluate sin 15 by using trig identity:
`2sin^2 a = 1 - cos 2a`.
Trig table of special arcs --> `cos (30) = sqrt3/2`
`2sin^2 (15) = 1 - cos (30) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`sin^2 (15) = (2 - sqrt3)/4`
`sin (15) = +- (2 - sqrt3)/2`
Since sin (15) is positive, then,
`sin (735) = sin (15) = sqrt(2 - sqrt3)/2`