What is the general solution for 0=4cos(120x) ?

The general solution for 0=4cos(120x) is x= pi/(240)+(pin)/(60),x= pi/(80)+(pin)/(60)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0=4cos(120x)

Solution

0 = 4 cos (120 x)

Solution

x = \frac{π}{240} + \frac{πn}{60}, x = \frac{π}{80} + \frac{πn}{60}

Degrees

x = 0.7 5^{\circ} + 3^{\circ} n, x = 2.2 5^{\circ} + 3^{\circ} n

Solution steps

0 = 4 cos (120 x)

Switch sides

4 cos (120 x) = 0

Divide both sides by

4

4 cos (120 x) = 0

Divide both sides by

4

\frac{4 cos ( 120 x )}{4} = \frac{0}{4}

Simplify

cos (120 x) = 0

cos (120 x) = 0

General solutions for

cos (120 x) = 0

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}

120 x = \frac{π}{2} + 2 πn, 120 x = \frac{3 π}{2} + 2 πn

120 x = \frac{π}{2} + 2 πn, 120 x = \frac{3 π}{2} + 2 πn

Solve

120 x = \frac{π}{2} + 2 πn : x = \frac{π}{240} + \frac{πn}{60}

120 x = \frac{π}{2} + 2 πn

Divide both sides by

120

120 x = \frac{π}{2} + 2 πn

Divide both sides by

120

\frac{120 x}{120} = \frac{\frac{π}{2}}{120} + \frac{2 πn}{120}

Simplify

\frac{120 x}{120} = \frac{\frac{π}{2}}{120} + \frac{2 πn}{120}

Simplify

\frac{120 x}{120} : x

\frac{120 x}{120}

Divide the numbers:

\frac{120}{120} = 1

= x

Simplify

\frac{\frac{π}{2}}{120} + \frac{2 πn}{120} : \frac{π}{240} + \frac{πn}{60}

\frac{\frac{π}{2}}{120} + \frac{2 πn}{120}

\frac{\frac{π}{2}}{120} = \frac{π}{240}

\frac{\frac{π}{2}}{120}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 120}

Multiply the numbers:

2 \cdot 120 = 240

= \frac{π}{240}

\frac{2 πn}{120} = \frac{πn}{60}

\frac{2 πn}{120}

Cancel the common factor:

2

= \frac{πn}{60}

= \frac{π}{240} + \frac{πn}{60}

x = \frac{π}{240} + \frac{πn}{60}

x = \frac{π}{240} + \frac{πn}{60}

x = \frac{π}{240} + \frac{πn}{60}

Solve

120 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{80} + \frac{πn}{60}

120 x = \frac{3 π}{2} + 2 πn

Divide both sides by

120

120 x = \frac{3 π}{2} + 2 πn

Divide both sides by

120

\frac{120 x}{120} = \frac{\frac{3 π}{2}}{120} + \frac{2 πn}{120}

Simplify

\frac{120 x}{120} = \frac{\frac{3 π}{2}}{120} + \frac{2 πn}{120}

Simplify

\frac{120 x}{120} : x

\frac{120 x}{120}

Divide the numbers:

\frac{120}{120} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{120} + \frac{2 πn}{120} : \frac{π}{80} + \frac{πn}{60}

\frac{\frac{3 π}{2}}{120} + \frac{2 πn}{120}

\frac{\frac{3 π}{2}}{120} = \frac{π}{80}

\frac{\frac{3 π}{2}}{120}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 120}

Multiply the numbers:

2 \cdot 120 = 240

= \frac{3 π}{240}

Cancel the common factor:

3

= \frac{π}{80}

\frac{2 πn}{120} = \frac{πn}{60}

\frac{2 πn}{120}

Cancel the common factor:

2

= \frac{πn}{60}

= \frac{π}{80} + \frac{πn}{60}

x = \frac{π}{80} + \frac{πn}{60}

x = \frac{π}{80} + \frac{πn}{60}

x = \frac{π}{80} + \frac{πn}{60}

x = \frac{π}{240} + \frac{πn}{60}, x = \frac{π}{80} + \frac{πn}{60}

Popular Examples

(2sin(x)-1)(cos(x)-sqrt(2))=0

(2 sin (x) - 1) (cos (x) - 2) = 0

7-6sin(x)=3+2sin(x)

7 - 6 sin (x) = 3 + 2 sin (x)

cos(θ)=(2*10^{-5})/(54*10^{-6)}

cos (θ) = \frac{2 \cdot 1 0 ^{- 5}}{54 \cdot 1 0 ^{- 6}}

sin(a)= 9/41

sin (a) = \frac{9}{41}

sin(x)= 10/300

sin (x) = \frac{10}{300}

Frequently Asked Questions (FAQ)

What is the general solution for 0=4cos(120x) ?
The general solution for 0=4cos(120x) is x= pi/(240)+(pin)/(60),x= pi/(80)+(pin)/(60)