What is the general solution for 1+cos(x)=0 ?

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

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1+cos(x)=0

1 + cos (x) = 0

x = π + 2 πn

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

1 + cos (x) = 0

Move

1

to the right side

1 + cos (x) = 0

Subtract

1

from both sides

1 + cos (x) - 1 = 0 - 1

Simplify

cos (x) = - 1

cos (x) = - 1

General solutions for

cos (x) = - 1

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 = π + 2 πn

x = π + 2 πn

tan^{2} (θ) = \frac{1}{3}

3 cot (x) - 1 = 0

cos (x) + 1 = - cos (x)

sin (2 θ) = - 1

sin^{2} (x) = \frac{3}{4}

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