What is the general solution for solvefor x,2cos(x)=sqrt(3) ?

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

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solvefor x,2cos(x)=sqrt(3)

solve for

x, 2 cos (x) = 3

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

Degrees

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

Solution steps

2 cos (x) = 3

Divide both sides by

2

2 cos (x) = 3

Divide both sides by

2

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

Simplify

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

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

General solutions for

cos (x) = \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}

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

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

41 sin^{2} (x) + 32 sin (x) - 9 = 0

cos (x - 3 0^{\circ}) = 2 sin (x)

sin (θ) - 3 cos (θ) = 2

sec^{2} (3 θ) cos^{2} (3 θ) = sec^{2} (3 θ) + cos^{2} (3 θ)

sin (x) = 0.04

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