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

The general solution for cos(3x)=(-sqrt(3))/2 is x=(5pi}{18}+(2pin)/3 ,x=(7pi)/(18)+\frac{2pin)/3

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

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

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

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

3 x = \frac{5 π}{6} + 2 πn, 3 x = \frac{7 π}{6} + 2 πn

Solve

3 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

2 cos (2 θ) - 10 sin (θ) - 2 = - 6 sin (θ) - 3

cos (θ) = csc (θ)

0 = sin^{2} (x) - sin (x)

cos (2 x) + cos (x) = 2

sec^{2} (θ) + 2 tan (θ) = 0

What is the general solution for cos(3x)=(-sqrt(3))/2 ?
The general solution for cos(3x)=(-sqrt(3))/2 is x=(5pi}{18}+(2pin)/3 ,x=(7pi)/(18)+\frac{2pin)/3