Question

How do you find the value of `sin 20(theta)` using the double angle identity?

Answer 1

Find sin (20) deg

Explanation:

Call sin 20 = t
Apply the trig formula: `sin 3a = 3sin a - 4sin^3 a`
`sin 60 = sqrt3/2 = 3t - 4t^3`
We get an equation of third deg in t = sin 20.
4t^3 - 3t + sqrt3/2 = 0
I ask someone to help find the real roots by graphing calculator. Mine was lost.
The answer should be: t = sin 20 = 0.342