What is the general solution for 2+cos(x)=2 ?

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

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2+cos(x)=2

2 + cos (x) = 2

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

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

2 + cos (x) = 2

Subtract

2

from both sides

2 + cos (x) - 2 = 2 - 2

Simplify

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

cos (\frac{π}{2} + x) = 0

4.1 = 4.2 cos (18 t) + 3

4 sin (x) - 13 = 2 cos^{2} (x) - 9

cos (θ) = - \frac{8}{11}

sin (θ) = \frac{3}{12}

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