What is the general solution for cos(x)+(sqrt(3))/2 =0 ?

The general solution for cos(x)+(sqrt(3))/2 =0 is x=(5pi)/6+2pin,x=(7pi)/6+2pin

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cos(x)+(sqrt(3))/2 =0

cos (x) + \frac{3}{2} = 0

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Degrees

x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (x) + \frac{3}{2} = 0

Move

\frac{3}{2}

to the right side

cos (x) + \frac{3}{2} = 0

Subtract

\frac{3}{2}

from both sides

cos (x) + \frac{3}{2} - \frac{3}{2} = 0 - \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{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

sin (6 x) = \frac{1}{2}

0 = 9 cos (2 θ)

θ, r = 2 + 4 cos (θ)

cos^{2} (x) = \frac{( 7 k - 6 )}{4}

5 - 3 csc^{2} (x) = 1

What is the general solution for cos(x)+(sqrt(3))/2 =0 ?
The general solution for cos(x)+(sqrt(3))/2 =0 is x=(5pi)/6+2pin,x=(7pi)/6+2pin