What is the general solution for 8cos(θ)-4sqrt(3)=0 ?

The general solution for 8cos(θ)-4sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin

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8cos(θ)-4sqrt(3)=0

8 cos (θ) - 43 = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

8 cos (θ) - 43 = 0

Move

43

to the right side

8 cos (θ) - 43 = 0

Add

43

to both sides

8 cos (θ) - 43 + 43 = 0 + 43

Simplify

8 cos (θ) = 43

8 cos (θ) = 43

Divide both sides by

8

8 cos (θ) = 43

Divide both sides by

8

\frac{8 cos ( θ )}{8} = \frac{4 3}{8}

Simplify

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{2}

General solutions for

cos (θ) = \frac{3}{2}

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}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

cos (x) = 1 + sin (x)

(tan (x) + 3) (cos (x) + 2) = 0

x, cos (y) + sin (x) = 1

cot (x) + 5 csc (x) = 6

csc^{2} (x) = 1

What is the general solution for 8cos(θ)-4sqrt(3)=0 ?
The general solution for 8cos(θ)-4sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin