What is the general solution for cos(x)= 1/2 sqrt(3) ?

The general solution for cos(x)= 1/2 sqrt(3) is x= pi/6+2pin,x=(11pi)/6+2pin

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cos(x)= 1/2 sqrt(3)

cos (x) = \frac{1}{2} 3

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

Solution steps

cos (x) = \frac{1}{2} 3

Simplify

\frac{1}{2} 3 : \frac{3}{2}

\frac{1}{2} 3

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 3}{2}

Multiply:

1 \cdot 3 = 3

= \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

sin (2 x - 1 0^{\circ}) = cos (x + 4 0^{\circ})

sec (θ) = - 37

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

2 sec^{2} (x) - 8 = 0

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

What is the general solution for cos(x)= 1/2 sqrt(3) ?
The general solution for cos(x)= 1/2 sqrt(3) is x= pi/6+2pin,x=(11pi)/6+2pin