Solve 2\sin x=\sqrt{3}

Evaluate

2 sin (x) = 3

Multiply both sides of the equation by \frac{1}{2}

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

Calculate

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

Multiply the numbers

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

Use the inverse trigonometric function

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

Calculate

x = \frac{π}{3} x = \frac{2 π}{3}

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

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

Solution

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

Alternative Form

x = {6 0^{\circ} + 36 0^{\circ} k 12 0^{\circ} + 36 0^{\circ} k, k \in Z

Alternative Form

x \approx {1.047198 + 2 kπ 2.094395 + 2 kπ, k \in Z

2\sin x=\sqrt{3}