What is the general solution for 1-cos(x)=0.5 ?

The general solution for 1-cos(x)=0.5 is x= pi/3+2pin,x=(5pi)/3+2pin

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1-cos(x)=0.5

1 - cos (x) = 0.5

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

1 - cos (x) = 0.5

Move

1

to the right side

1 - cos (x) = 0.5

Subtract

1

from both sides

1 - cos (x) - 1 = 0.5 - 1

Simplify

- cos (x) = - 0.5

- cos (x) = - 0.5

Divide both sides by

- 1

- cos (x) = - 0.5

Divide both sides by

- 1

\frac{- cos ( x )}{- 1} = \frac{- 0.5}{- 1}

Simplify

cos (x) = 0.5

cos (x) = 0.5

General solutions for

cos (x) = 0.5

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

arctan (100 x) - arctan (x) = 4 5^{\circ}

tan^{2} (x) - 9 = 0

2 = - 4 - 3 csc (θ)

x, 3 tan (2 x) = - 1

1 + sin^{2} (x) = 0

What is the general solution for 1-cos(x)=0.5 ?
The general solution for 1-cos(x)=0.5 is x= pi/3+2pin,x=(5pi)/3+2pin