Find solutions for:

$$ sin (2x + \frac{\pi}{3}) = 1/2 $$

I've placed your equation on a new line and put two dollar signs on either side to have it render nicely.
Use \frac{\pi}{3} to get a pretty fraction too!
Good point. Done! Thanks @Collin Li.

1 Answer

Best answer

Angle to give the sine exact value of 1/2 is 30º or π/6 (radians)

Sine is positive in quadrants 1 and 2, so π/6 or 5π/6 are possible angles for sine

Hence: 2x + π/3 = π/6, 5π/6
2x = -π/6, π/2
x = -π/12, π/4

Since the period of this function is π (coefficient of 2 yields p = 2π/2 = π), the general solutions are:

x = -π/12 + kπ
x = π/4 + kπ
where k is any integer