Solve sin(2x)=1/2

Evaluate

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

Use the inverse trigonometric function

2 x = arcsin (\frac{1}{2})

Calculate

2 x = \frac{π}{6} 2 x = \frac{5 π}{6}

Add the period of 2 kπ, k \in Z to find all solutions

2 x = \frac{π}{6} + 2 kπ, k \in Z 2 x = \frac{5 π}{6} + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{π}{12} + kπ, k \in Z 2 x = \frac{5 π}{6} + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{π}{12} + kπ, k \in Z x = \frac{5 π}{12} + kπ, k \in Z

Solution

x = {\frac{π}{12} + kπ \frac{5 π}{12} + kπ, k \in Z

Alternative Form

x = {1 5^{\circ} + 18 0^{\circ} k 7 5^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.261799 + kπ 1.308997 + kπ, k \in Z

Solve the equation