Question

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

Answer 1

Find sin (pi/6)

Ans: 1/2

Explanation:

Trig Table of special Arcs gives --> sin pi/6 = 1/2.
However if you still want to find it by using trig identities, then this is the popular way.
Apply the trig identity: `cos 2a = 1 - 2sin^2 a`
`cos ((2pi)/6) = cos pi/3 = 1/2 = 1 - 2sin^2 (pi/6)`
`2sin^2 (pi/6) = 1 - 1/2 = 1/2`
`sin^2 (pi/6) = 1/4`
`sin (pi/6) = +- 1/2.`
Since `pi/6` is in Quadrant I, its sin is positive , then
`sin (pi/6) = 1/2`