What is the general solution for cos(x)= 1/2 ,0<= x<2pi ?

The general solution for cos(x)= 1/2 ,0<= x<2pi is x= pi/3 ,x=(5pi)/3

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cos(x)= 1/2 ,0<= x<2pi

cos (x) = \frac{1}{2}, 0 \leq x < 2 π

x = \frac{π}{3}, x = \frac{5 π}{3}

Degrees

x = 6 0^{\circ}, x = 30 0^{\circ}

Solution steps

cos (x) = \frac{1}{2}, 0 \leq x < 2 π

General solutions for

cos (x) = \frac{1}{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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{3}, x = \frac{5 π}{3}

sin (b) = \frac{12}{13}

3 = 1 + sec (x)

3 sin^{2} (x) - 7 sin (x) = 6

2 sin (x) (cos (x) - sin (x)) + (cos (x) - sin (x)) = 0

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

What is the general solution for cos(x)= 1/2 ,0<= x<2pi ?
The general solution for cos(x)= 1/2 ,0<= x<2pi is x= pi/3 ,x=(5pi)/3