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

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

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3=3-3cos(θ)

3 = 3 - 3 cos (θ)

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 - 3 cos (θ)

Switch sides

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

a, tan (a) - tan (b) = 0

cos (x) = - cos (\frac{π}{7})

5 cos (x) - sin (x) = 1

tan (2 θ) = - 1.75

cos (x) = \frac{3}{2}, tan (x)

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