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

The general solution for (cos(θ))(cos(θ)+1)=0 is θ= pi/2+2pin,θ=(3pi)/2+2pin,θ=pi+2pin

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(cos(θ))(cos(θ)+1)=0

(cos (θ)) (cos (θ) + 1) = 0

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

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n, θ = 27 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

(cos (θ)) (cos (θ) + 1) = 0

Solving each part separately

cos (θ) = 0 or cos (θ) + 1 = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

cos (θ) = 0

General solutions for

cos (θ) = 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}

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

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

cos (θ) + 1 = 0 : θ = π + 2 πn

cos (θ) + 1 = 0

Move

1

to the right side

cos (θ) + 1 = 0

Subtract

1

from both sides

cos (θ) + 1 - 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

Combine all the solutions

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

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

- 2 tan (x) + 1 = 23 + 1

sin (x - \frac{π}{3}) = \frac{1}{2}

sec^{2} (x) - 1 \cdot sec^{2} (x) = sin^{2} (x)

\frac{17}{8} sin (82 x + 1.326) = 0

What is the general solution for (cos(θ))(cos(θ)+1)=0 ?
The general solution for (cos(θ))(cos(θ)+1)=0 is θ= pi/2+2pin,θ=(3pi)/2+2pin,θ=pi+2pin