What is the general solution for 5(cos(θ)+1)=5 ?

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

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5(cos(θ)+1)=5

5 (cos (θ) + 1) = 5

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

Degrees

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

Solution steps

5 (cos (θ) + 1) = 5

Divide both sides by

5

5 (cos (θ) + 1) = 5

Divide both sides by

5

\frac{5 ( cos ( θ ) + 1 )}{5} = \frac{5}{5}

Simplify

cos (θ) + 1 = 1

cos (θ) + 1 = 1

Move

1

to the right side

cos (θ) + 1 = 1

Subtract

1

from both sides

cos (θ) + 1 - 1 = 1 - 1

Simplify

cos (θ) = 0

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

sin (2 x) + \frac{3}{2} = 0

tan (x) = \frac{1}{2}

7 cos (x) + 3 = 3 cos (x) + 2

2 sin (2 θ) + 1 = 0

sin (2 x) - 2 sin (x) = 0

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