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Trigonometry · Trigonometric-Equations

Solve sin(x) = 3/5

\sin{\left(x \right)} = \frac{3}{5}

Step by step

  1. \sin{\left(x \right)} = \frac{3}{5}

    Start from the equation as given.

  2. \sin{\left(x \right)} - \frac{3}{5} = 0

    Bring everything to one side.

  3. \sin{\left(x \right)} - \frac{3}{5} = 0

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

  4. \left\{2 n \pi + \operatorname{asin}{\left(\frac{3}{5} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi - \operatorname{asin}{\left(\frac{3}{5} \right)} + \pi\; \middle|\; n \in \mathbb{Z}\right\}

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

  5. x = \pi - \operatorname{asin}{\left(\frac{3}{5} \right)} \approx 2.4981 ,\; x = \operatorname{asin}{\left(\frac{3}{5} \right)} \approx 0.64350

    Solve for the variable.

Reveal the answer
x = \pi - \operatorname{asin}{\left(\frac{3}{5} \right)} ,\; x = \operatorname{asin}{\left(\frac{3}{5} \right)}