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Trigonometry · Trigonometric-Equations

Solve cos(x) = 0

\cos{\left(x \right)} = 0

Step by step

  1. \cos{\left(x \right)} = 0

    Start from the equation as given.

  2. \cos{\left(x \right)} = 0

    Bring everything to one side.

  3. \cos{\left(x \right)} = 0

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

  4. \left\{2 n \pi + \frac{\pi}{2}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + \frac{3 \pi}{2}\; \middle|\; n \in \mathbb{Z}\right\}

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

  5. x = \frac{\pi}{2} \approx 1.5708 ,\; x = \frac{3 \pi}{2} \approx 4.7124

    Solve for the variable.

Reveal the answer
x = \frac{\pi}{2} ,\; x = \frac{3 \pi}{2}