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

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

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0=1+cos(θ)

0 = 1 + cos (θ)

θ = π + 2 πn

Degrees

θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = 1 + cos (θ)

Switch sides

1 + cos (θ) = 0

Move

1

to the right side

1 + cos (θ) = 0

Subtract

1

from both sides

1 + cos (θ) - 1 = 0 - 1

Simplify

cos (θ) = - 1

cos (θ) = - 1

General solutions for

cos (θ) = - 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}

θ = π + 2 πn

θ = π + 2 πn

3 cos^{2} (x) + 1 = 4 sin (x)

[2 sin (4 x) - 1] \cdot [1 + tan (x)] = 0

cos^{2} (x) = 2 cos (x)

sin (4 θ) = \frac{3}{2}

2 sin (θ) = - 0.684

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