Solve 4 sin2x=3 - ScanMath

Evaluate

4 sin (2 x) = 3

Multiply both sides of the equation by \frac{1}{4}

4 sin (2 x) \times \frac{1}{4} = 3 \times \frac{1}{4}

Calculate

sin (2 x) = 3 \times \frac{1}{4}

Multiply the numbers

sin (2 x) = \frac{3}{4}

Use the inverse trigonometric function

2 x = arcsin (\frac{3}{4})

Calculate

2 x = arcsin (\frac{3}{4}) 2 x = - arcsin (\frac{3}{4}) + π

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

2 x = arcsin (\frac{3}{4}) + 2 kπ, k \in Z 2 x = - arcsin (\frac{3}{4}) + π + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{arcsin ( \frac{3}{4} )}{2} + kπ, k \in Z 2 x = - arcsin (\frac{3}{4}) + π + 2 kπ, k \in Z

Calculate

More Steps

x = \frac{arcsin ( \frac{3}{4} )}{2} + kπ, k \in Z x = \frac{- arcsin ( \frac{3}{4} ) + π}{2} + kπ, k \in Z

Solution

x = ⎩ ⎨ ⎧ \frac{a r c s i n ( \frac{3}{4} )}{2} + kπ \frac{- a r c s i n ( \frac{3}{4} ) + π}{2} + kπ, k \in Z

Alternative Form

x \approx {24.29518 9^{\circ} + 18 0^{\circ} k 65.70481 1^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.424031 + kπ 1.146765 + kπ, k \in Z

Solve the equation