Find solutions for:

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

Asked May 20, 2014 by anonymous edited May 21, 2014 by Community

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

Answered May 20, 2014 by Collin Li (56,060 points) selected May 20, 2014 by Community

## Find solutions for sin (2x + pi/3) = 1/2

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