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

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

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2cos(a)=sqrt(3)

2 cos (a) = 3

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

Degrees

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

Solution steps

2 cos (a) = 3

Divide both sides by

2

2 cos (a) = 3

Divide both sides by

2

\frac{2 cos ( a )}{2} = \frac{3}{2}

Simplify

cos (a) = \frac{3}{2}

cos (a) = \frac{3}{2}

General solutions for

cos (a) = \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}

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

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

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

sin^{2} (4 x) = 1

sinh (x) = \frac{2}{3}

cos (α_{2}) = \frac{1}{14}, 0 \leq α_{2} \leq 2 π

sin (2 x + 60) = \frac{1}{2}

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