What is the general solution for 5/2 =2+cos(x+(2pi)/3) ?

The general solution for 5/2 =2+cos(x+(2pi)/3) is x=2pin-pi/3 ,x=2pin+pi

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5/2 =2+cos(x+(2pi)/3)

\frac{5}{2} = 2 + cos (x + \frac{2 π}{3})

x = 2 πn - \frac{π}{3}, x = 2 πn + π

Solution steps

\frac{5}{2} = 2 + cos (x + \frac{2 π}{3})

Switch sides

2 + cos (x + \frac{2 π}{3}) = \frac{5}{2}

Move

2

to the right side

cos (x + \frac{2 π}{3}) = \frac{1}{2}

General solutions for

cos (x + \frac{2 π}{3}) = \frac{1}{2}

x + \frac{2 π}{3} = \frac{π}{3} + 2 πn, x + \frac{2 π}{3} = \frac{5 π}{3} + 2 πn

Solve

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

Solve

x + \frac{2 π}{3} = \frac{5 π}{3} + 2 πn : x = 2 πn + π

x = 2 πn - \frac{π}{3}, x = 2 πn + π

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

2 sec (x) = 0

sin^{2} (θ) cos^{2} (θ) = 0, 0 \leq θ < 2 π

tan (θ) + 2 = 0

2 sin (2 x) + cos (2 x) = 0

What is the general solution for 5/2 =2+cos(x+(2pi)/3) ?
The general solution for 5/2 =2+cos(x+(2pi)/3) is x=2pin-pi/3 ,x=2pin+pi