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Trigonometry · Trigonometric-Equations

Solve 2·sin(x) - 1 = 0

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

2 \sin{\left(x \right)} - 1 = 0
Start from the equation as given.
2 \sin{\left(x \right)} - 1 = 0
Bring everything to one side.
2 \sin{\left(x \right)} - 1 = 0
Isolate the trig function, then read the reference angle off the unit circle. Solutions repeat every period.
\left\{2 n \pi + \frac{\pi}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + \frac{5 \pi}{6}\; \middle|\; n \in \mathbb{Z}\right\}
General solution over the reals (n is any integer).
x = \frac{\pi}{6} \approx 0.52360 ,\; x = \frac{5 \pi}{6} \approx 2.6180
Solve for the variable.

Reveal the answer

x = \frac{\pi}{6} ,\; x = \frac{5 \pi}{6}