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

The general solution for 2cos(3x)=sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3

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2cos(3x)=sqrt(2)

Solution

2 cos (3 x) = 2

Solution

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

Degrees

x = 1 5^{\circ} + 12 0^{\circ} n, x = 10 5^{\circ} + 12 0^{\circ} n

Solution steps

2 cos (3 x) = 2

Divide both sides by

2

2 cos (3 x) = 2

Divide both sides by

2

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

Simplify

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

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

General solutions for

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

3 x = \frac{π}{4} + 2 πn, 3 x = \frac{7 π}{4} + 2 πn

3 x = \frac{π}{4} + 2 πn, 3 x = \frac{7 π}{4} + 2 πn

Solve

3 x = \frac{π}{4} + 2 πn : x = \frac{π}{12} + \frac{2 πn}{3}

3 x = \frac{π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{π}{4} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3} : \frac{π}{12} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}

Solve

3 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{12} + \frac{2 πn}{3}

3 x = \frac{7 π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{7 π}{4} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3} : \frac{7 π}{12} + \frac{2 πn}{3}

\frac{\frac{7 π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{7 π}{4}}{3} = \frac{7 π}{12}

\frac{\frac{7 π}{4}}{3}

Apply the fraction rule:

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

= \frac{7 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{7 π}{12}

= \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

Popular Examples

tan^2(x/2)-tan(x/2)-2=0

tan^{2} (\frac{x}{2}) - tan (\frac{x}{2}) - 2 = 0

tan(x)=(-3)/4

tan (x) = \frac{- 3}{4}

sin(x)=-2sin^2(x)

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

sqrt(3)cos(θ)=sin(θ)

3 cos (θ) = sin (θ)

csc(θ)= 4/3

csc (θ) = \frac{4}{3}

Frequently Asked Questions (FAQ)

What is the general solution for 2cos(3x)=sqrt(2) ?
The general solution for 2cos(3x)=sqrt(2) is x= pi/(12)+(2pin)/3 ,x=(7pi}{12}+\frac{2pin)/3