Question

How do you use the half angle identity to find exact value of sin^3(pi/6)?

Answer 1

Find exact value of `sin^3 (pi/6)`

Ans: `1/8`

Explanation:

From the trig identity: `sin 3x = 3sin x - 4sin^3 x`, we get:
`4sin^3 x = 3sin x - sin (3x)`.
Replace x by `(pi/6)`, and 3x by `((3pi)/6) = (pi/2)`, we get:
`4sin^3 (pi/6) = 3sin (pi/6) - sin (pi/2)`
`4sin^3 (pi/6) = 3(1/2) - sin (pi/2) = 3/2 - 1 = 1/2`
`sin^3 (pi/6) = 1/8`