What is the general solution for 2cos(α)=sqrt(3) ?

The general solution for 2cos(α)=sqrt(3) is α= pi/6+2pin,α=(11pi)/6+2pin

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2cos(α)=sqrt(3)

2 cos (α) = 3

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

Degrees

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

Solution steps

2 cos (α) = 3

Divide both sides by

2

2 cos (α) = 3

Divide both sides by

2

\frac{2 cos ( α )}{2} = \frac{3}{2}

Simplify

cos (α) = \frac{3}{2}

cos (α) = \frac{3}{2}

General solutions for

cos (α) = \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}

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

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

(csc (θ) + 2) (3 cot (θ) + 3) = 0

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

2 sin^{2} (2 x) - cos (2 x) - 1 = 0

2 \cdot cos (x) - 1 = 0

cos (x) + 3 sin (x) = 2

What is the general solution for 2cos(α)=sqrt(3) ?
The general solution for 2cos(α)=sqrt(3) is α= pi/6+2pin,α=(11pi)/6+2pin