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

The general solution for cos(2/3 x-pi/2)-1=0 is x=3pin+(3pi)/4

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cos(2/3 x-pi/2)-1=0

cos (\frac{2}{3} x - \frac{π}{2}) - 1 = 0

x = 3 πn + \frac{3 π}{4}

Solution steps

cos (\frac{2}{3} x - \frac{π}{2}) - 1 = 0

Move

1

to the right side

cos (\frac{2}{3} x - \frac{π}{2}) = 1

General solutions for

cos (\frac{2}{3} x - \frac{π}{2}) = 1

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn

Solve

\frac{2}{3} x - \frac{π}{2} = 0 + 2 πn : x = 3 πn + \frac{3 π}{4}

x = 3 πn + \frac{3 π}{4}

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

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

- sin (2 x) \cdot 2 = 0

sin (x) = 3 cos (x)

cos (2 t) = cos (t)

What is the general solution for cos(2/3 x-pi/2)-1=0 ?
The general solution for cos(2/3 x-pi/2)-1=0 is x=3pin+(3pi)/4