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

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

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3=-3cos(θ)

3 = - 3 cos (θ)

θ = π + 2 πn

Degrees

θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

3 = - 3 cos (θ)

Switch sides

- 3 cos (θ) = 3

Divide both sides by

- 3

- 3 cos (θ) = 3

Divide both sides by

- 3

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

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

2 cos (θ) - 3 = 0, 0 \leq θ \leq 2 π

- 4 sin (x) = cos^{2} (x) + 1, 0 \leq x \leq 2 π

3 sin (x) - 3 cos (x) = 3

tan (2 x) cos (2 x) + cot (2 x) sin (2 x) = 1

sin^{2} (2 x) - cos^{2} (2 x) = \frac{1}{2}

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