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

The general solution for -2cos(2x)=sqrt(3) is x=(5pi)/(12)+pin,x=(7pi)/(12)+pin

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Popular >

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

Solution

- 2 cos (2 x) = 3

Solution

x = \frac{5 π}{12} + πn, x = \frac{7 π}{12} + πn

Degrees

x = 7 5^{\circ} + 18 0^{\circ} n, x = 10 5^{\circ} + 18 0^{\circ} n

Solution steps

- 2 cos (2 x) = 3

Divide both sides by

- 2

- 2 cos (2 x) = 3

Divide both sides by

- 2

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

Simplify

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

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

General solutions for

cos (2 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}

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

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

Solve

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

2 x = \frac{5 π}{6} + 2 πn

Divide both sides by

2

2 x = \frac{5 π}{6} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2} : \frac{5 π}{12} + πn

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

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

x = \frac{5 π}{12} + πn

Solve

2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{12} + πn

2 x = \frac{7 π}{6} + 2 πn

Divide both sides by

2

2 x = \frac{7 π}{6} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{7 π}{6}}{2} + \frac{2 πn}{2} : \frac{7 π}{12} + πn

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

\frac{\frac{7 π}{6}}{2} = \frac{7 π}{12}

\frac{\frac{7 π}{6}}{2}

Apply the fraction rule:

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

= \frac{7 π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{7 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

x = \frac{5 π}{12} + πn, x = \frac{7 π}{12} + πn

Popular Examples

(tan(x)-1)(2sin(x)-sqrt(3))=0

(tan (x) - 1) (2 sin (x) - 3) = 0

tan(θ)(1+tan^2(θ))=0

tan (θ) (1 + tan^{2} (θ)) = 0

tan(x)=9

tan (x) = 9

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

sin (2 x) = 0, 0 \leq x \leq 2 π

1/2 =sin^2(x)

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

Frequently Asked Questions (FAQ)

What is the general solution for -2cos(2x)=sqrt(3) ?
The general solution for -2cos(2x)=sqrt(3) is x=(5pi)/(12)+pin,x=(7pi)/(12)+pin