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

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

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

cos (x) = 0, 0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

Degrees

x = 9 0^{\circ}, x = 27 0^{\circ}

Solution steps

cos (x) = 0, 0 \leq x < 2 π

General solutions for

cos (x) = 0

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}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

cos^{3} (x) - 2 cos^{2} (x) + cos (x) - 2 = 0

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

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

- sin (2 x) (2) = 0

cos (5 x - 21) = sin (13 - 3 x)

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