What is the general solution for 0=3sin(x-1/2 pi)+2 ?

The general solution for 0=3sin(x-1/2 pi)+2 is x=-0.72972…+2pin+pi/2 ,x=pi+0.72972…+2pin+pi/2

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0=3sin(x-1/2 pi)+2

0 = 3 sin (x - \frac{1}{2} π) + 2

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

Solution steps

0 = 3 sin (x - \frac{1}{2} π) + 2

Switch sides

3 sin (x - \frac{1}{2} π) + 2 = 0

Move

2

to the right side

3 sin (x - \frac{1}{2} π) = - 2

Divide both sides by

3

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

Apply trig inverse properties

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn, x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn

Solve

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn : x = - arcsin (\frac{2}{3}) + 2 πn + \frac{π}{2}

Solve

x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn : x = π + arcsin (\frac{2}{3}) + 2 πn + \frac{π}{2}

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

Show solutions in decimal form

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

2 sin^{2} (x) = 3 sin (x)

5 + 2 sin (x) - 7 = 0

0 = 4 sin (4 x + 3 π)

0.5 = 1 - sin (θ)

θ, r = 6 sin (2 θ)

What is the general solution for 0=3sin(x-1/2 pi)+2 ?
The general solution for 0=3sin(x-1/2 pi)+2 is x=-0.72972…+2pin+pi/2 ,x=pi+0.72972…+2pin+pi/2