What is the general solution for 3sin(2x)=2,0<= x<= pi ?

The general solution for 3sin(2x)=2,0<= x<= pi is x=(0.72972…)/2 ,x=(pi-0.72972…)/2

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3sin(2x)=2,0<= x<= pi

3 sin (2 x) = 2, 0 \leq x \leq π

x = \frac{0.72972 \dots}{2}, x = \frac{π - 0.72972 \dots}{2}

Solution steps

3 sin (2 x) = 2, 0 \leq x \leq π

Divide both sides by

3

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

Apply trig inverse properties

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

Solve

2 x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{arcsin ( \frac{2}{3} )}{2} + πn

Solve

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

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

Solutions for the range

0 \leq x \leq π

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

Show solutions in decimal form

x = \frac{0.72972 \dots}{2}, x = \frac{π - 0.72972 \dots}{2}

cos (θ) = \frac{2}{2.24}

cot (α) = \frac{2}{3}

- 900 cos (30 x) = 0

sin^{2} (x) = \frac{( 9 m - 9 )}{7}

sin (x) = 0.55669

What is the general solution for 3sin(2x)=2,0<= x<= pi ?
The general solution for 3sin(2x)=2,0<= x<= pi is x=(0.72972…)/2 ,x=(pi-0.72972…)/2