Solve sin(3x)= 1/2

Evaluate

sin (3 x) = \frac{1}{2}

Use the inverse trigonometric function

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

Calculate

3 x = \frac{π}{6} 3 x = \frac{5 π}{6}

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

3 x = \frac{π}{6} + 2 kπ, k \in Z 3 x = \frac{5 π}{6} + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{π}{18} + \frac{2 kπ}{3}, k \in Z 3 x = \frac{5 π}{6} + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{π}{18} + \frac{2 kπ}{3}, k \in Z x = \frac{5 π}{18} + \frac{2 kπ}{3}, k \in Z

Solution

x = {\frac{π}{18} + \frac{2 kπ}{3} \frac{5 π}{18} + \frac{2 kπ}{3}, k \in Z

Alternative Form

x = {1 0^{\circ} + 12 0^{\circ} k 5 0^{\circ} + 12 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.174533 + \frac{2 kπ}{3} 0.872665 + \frac{2 kπ}{3}, k \in Z

Solve the equation