What is the general solution for 3-3cos(θ)=3 ?

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

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3-3cos(θ)=3

3 - 3 cos (θ) = 3

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

3 - 3 cos (θ) = 3

Subtract

3

from both sides

3 - 3 cos (θ) - 3 = 3 - 3

Simplify

- 3 cos (θ) = 0

Divide both sides by

- 3

- 3 cos (θ) = 0

Divide both sides by

- 3

\frac{- 3 cos ( θ )}{- 3} = \frac{0}{- 3}

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

\frac{1 - tanh ( 2 x )}{1 + tanh ( 2 x )} = 2

5 sin (θ) - 5 cos (θ) = 2

2 sin^{2} (θ) - 2 = cos^{2} (θ), 0 \leq θ < 2 π

sin (a) = \frac{1}{2}

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

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