What is the general solution for 2cos(6x)+sqrt(3)=0 ?

The general solution for 2cos(6x)+sqrt(3)=0 is x=(5pi}{36}+(pin)/3 ,x=(7pi)/(36)+\frac{pin)/3

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Popular Trigonometry >

2cos(6x)+sqrt(3)=0

Solution

2 cos (6 x) + 3 = 0

Solution

x = \frac{5 π}{36} + \frac{πn}{3}, x = \frac{7 π}{36} + \frac{πn}{3}

Degrees

x = 2 5^{\circ} + 6 0^{\circ} n, x = 3 5^{\circ} + 6 0^{\circ} n

Solution steps

2 cos (6 x) + 3 = 0

Move

3

to the right side

2 cos (6 x) + 3 = 0

Subtract

3

from both sides

2 cos (6 x) + 3 - 3 = 0 - 3

Simplify

2 cos (6 x) = - 3

2 cos (6 x) = - 3

Divide both sides by

2

2 cos (6 x) = - 3

Divide both sides by

2

\frac{2 cos ( 6 x )}{2} = \frac{- 3}{2}

Simplify

cos (6 x) = - \frac{3}{2}

cos (6 x) = - \frac{3}{2}

General solutions for

cos (6 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}

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

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

Solve

6 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{36} + \frac{πn}{3}

6 x = \frac{5 π}{6} + 2 πn

Divide both sides by

6

6 x = \frac{5 π}{6} + 2 πn

Divide both sides by

6

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

Simplify

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

Simplify

\frac{6 x}{6} : x

\frac{6 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{6} + \frac{2 πn}{6} : \frac{5 π}{36} + \frac{πn}{3}

\frac{\frac{5 π}{6}}{6} + \frac{2 πn}{6}

\frac{\frac{5 π}{6}}{6} = \frac{5 π}{36}

\frac{\frac{5 π}{6}}{6}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{6 \cdot 6}

Multiply the numbers:

6 \cdot 6 = 36

= \frac{5 π}{36}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Cancel the common factor:

2

= \frac{πn}{3}

= \frac{5 π}{36} + \frac{πn}{3}

x = \frac{5 π}{36} + \frac{πn}{3}

x = \frac{5 π}{36} + \frac{πn}{3}

x = \frac{5 π}{36} + \frac{πn}{3}

Solve

6 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{36} + \frac{πn}{3}

6 x = \frac{7 π}{6} + 2 πn

Divide both sides by

6

6 x = \frac{7 π}{6} + 2 πn

Divide both sides by

6

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

Simplify

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

Simplify

\frac{6 x}{6} : x

\frac{6 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= x

Simplify

\frac{\frac{7 π}{6}}{6} + \frac{2 πn}{6} : \frac{7 π}{36} + \frac{πn}{3}

\frac{\frac{7 π}{6}}{6} + \frac{2 πn}{6}

\frac{\frac{7 π}{6}}{6} = \frac{7 π}{36}

\frac{\frac{7 π}{6}}{6}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{7 π}{6 \cdot 6}

Multiply the numbers:

6 \cdot 6 = 36

= \frac{7 π}{36}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Cancel the common factor:

2

= \frac{πn}{3}

= \frac{7 π}{36} + \frac{πn}{3}

x = \frac{7 π}{36} + \frac{πn}{3}

x = \frac{7 π}{36} + \frac{πn}{3}

x = \frac{7 π}{36} + \frac{πn}{3}

x = \frac{5 π}{36} + \frac{πn}{3}, x = \frac{7 π}{36} + \frac{πn}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2cos(6x)+sqrt(3)=0 ?
The general solution for 2cos(6x)+sqrt(3)=0 is x=(5pi}{36}+(pin)/3 ,x=(7pi)/(36)+\frac{pin)/3