What is the general solution for -6cos(θ)+4=4 ?

The general solution for -6cos(θ)+4=4 is θ= pi/2+2pin,θ=(3pi)/2+2pin

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-6cos(θ)+4=4

- 6 cos (θ) + 4 = 4

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

- 6 cos (θ) + 4 = 4

Subtract

4

from both sides

- 6 cos (θ) + 4 - 4 = 4 - 4

Simplify

- 6 cos (θ) = 0

Divide both sides by

- 6

- 6 cos (θ) = 0

Divide both sides by

- 6

\frac{- 6 cos ( θ )}{- 6} = \frac{0}{- 6}

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

4 cos (x) = - sin^{2} (x) + 4

7 cos^{2} (θ) + 5 = 2 sin (θ) + 7

1 - cos (2 x) = 1 + cos (2 x)

5 cos^{2} (x) - 10 cos (x) + 5 = 0

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

What is the general solution for -6cos(θ)+4=4 ?
The general solution for -6cos(θ)+4=4 is θ= pi/2+2pin,θ=(3pi)/2+2pin