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

csc^{2} (x) = 3 csc (x) + 4

4 cot (2 θ) = 0

sin (6 0^{\circ}) = cos (x + 1 0^{\circ})

sin (2 x) = 682

0 = 5 \cdot sin (2 π \cdot (- 0.25 - 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