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Trigonometry · Trigonometric-Equations

Solve sin(2x) = 1/2

\sin{\left(2 x \right)} = \frac{1}{2}

Step by step

  1. \sin{\left(2 x \right)} = \frac{1}{2}

    Start from the equation as given.

  2. \sin{\left(2 x \right)} - \frac{1}{2} = 0

    Bring everything to one side.

  3. \sin{\left(2 x \right)} - \frac{1}{2} = 0

    Isolate the trig function, then read the reference angle off the unit circle. Solutions repeat every period.

  4. \left\{n \pi + \frac{\pi}{12}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{n \pi + \frac{5 \pi}{12}\; \middle|\; n \in \mathbb{Z}\right\}

    General solution over the reals (n is any integer).

  5. x = \frac{\pi}{12} \approx 0.26180 ,\; x = \frac{5 \pi}{12} \approx 1.3090

    Solve for the variable.

Reveal the answer
x = \frac{\pi}{12} ,\; x = \frac{5 \pi}{12}