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

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

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

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

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}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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 (2 x) = - 3 sin (x)

2 cos (\frac{x + π}{6}) = 1, 0 < x < 2 π

tan^{2} (x) + sec (x) - 1 = 0

2 cos (x) sin (x) = cos (x)

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

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