Evaluate: sin(pi/6 + 2x).

Question

Pretty much same as title. I know the answer, just can't find how to get to it. Thanks

Answer 1

I'm unsure if this problem is written accurately but if it is, you would need to use the sum identity to evaluate it. The sum identity for sine is:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Since sin(π/6) = 1/2 and cos(π/6) = √3/2 then sin(π/6 + 2x) = 1/2(cos(2x)) + √3/2(sin(2x))