What is the general solution for 2cos(3θ)-1=0 ?

The general solution for 2cos(3θ)-1=0 is θ= pi/9+(2pin)/3 ,θ=(5pi)/9+(2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(3θ)-1=0

Solution

2 cos (3 θ) - 1 = 0

Solution

θ = \frac{π}{9} + \frac{2 πn}{3}, θ = \frac{5 π}{9} + \frac{2 πn}{3}

Degrees

θ = 2 0^{\circ} + 12 0^{\circ} n, θ = 10 0^{\circ} + 12 0^{\circ} n

Solution steps

2 cos (3 θ) - 1 = 0

Move

1

to the right side

2 cos (3 θ) - 1 = 0

Add

1

to both sides

2 cos (3 θ) - 1 + 1 = 0 + 1

Simplify

2 cos (3 θ) = 1

2 cos (3 θ) = 1

Divide both sides by

2

2 cos (3 θ) = 1

Divide both sides by

2

\frac{2 cos ( 3 θ )}{2} = \frac{1}{2}

Simplify

cos (3 θ) = \frac{1}{2}

cos (3 θ) = \frac{1}{2}

General solutions for

cos (3 θ) = \frac{1}{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 θ = \frac{π}{3} + 2 πn, 3 θ = \frac{5 π}{3} + 2 πn

3 θ = \frac{π}{3} + 2 πn, 3 θ = \frac{5 π}{3} + 2 πn

Solve

3 θ = \frac{π}{3} + 2 πn : θ = \frac{π}{9} + \frac{2 πn}{3}

3 θ = \frac{π}{3} + 2 πn

Divide both sides by

3

3 θ = \frac{π}{3} + 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{π}{3}}{3} + \frac{2 πn}{3} : \frac{π}{9} + \frac{2 πn}{3}

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

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{π}{9} + \frac{2 πn}{3}

θ = \frac{π}{9} + \frac{2 πn}{3}

θ = \frac{π}{9} + \frac{2 πn}{3}

θ = \frac{π}{9} + \frac{2 πn}{3}

Solve

3 θ = \frac{5 π}{3} + 2 πn : θ = \frac{5 π}{9} + \frac{2 πn}{3}

3 θ = \frac{5 π}{3} + 2 πn

Divide both sides by

3

3 θ = \frac{5 π}{3} + 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3} : \frac{5 π}{9} + \frac{2 πn}{3}

\frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{3}}{3} = \frac{5 π}{9}

\frac{\frac{5 π}{3}}{3}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{5 π}{9}

= \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{π}{9} + \frac{2 πn}{3}, θ = \frac{5 π}{9} + \frac{2 πn}{3}

Popular Examples

cos(4x)=cos(8x)

cos (4 x) = cos (8 x)

cos(2x)-cos(x)=2

cos (2 x) - cos (x) = 2

4sin(2x)+2sqrt(3)=0

4 sin (2 x) + 23 = 0

solvefor x,3=18cos(x)solve for

x, 3 = 18 cos (x)

solvefor x,2sin((pi(x-2))/6)=1 solve for

x, 2 sin (\frac{π ( x - 2 )}{6}) = 1

Frequently Asked Questions (FAQ)

What is the general solution for 2cos(3θ)-1=0 ?
The general solution for 2cos(3θ)-1=0 is θ= pi/9+(2pin)/3 ,θ=(5pi)/9+(2pin)/3