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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos(120t)=0

Solution

4 cos (120 t) = 0

Solution

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

Degrees

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

Solution steps

4 cos (120 t) = 0

Divide both sides by

4

4 cos (120 t) = 0

Divide both sides by

4

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

Simplify

cos (120 t) = 0

cos (120 t) = 0

General solutions for

cos (120 t) = 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 t = \frac{π}{2} + 2 πn, 120 t = \frac{3 π}{2} + 2 πn

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

Solve

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

120 t = \frac{π}{2} + 2 πn

Divide both sides by

120

120 t = \frac{π}{2} + 2 πn

Divide both sides by

120

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

Simplify

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

Simplify

\frac{120 t}{120} : t

\frac{120 t}{120}

Divide the numbers:

\frac{120}{120} = 1

= t

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}

t = \frac{π}{240} + \frac{πn}{60}

t = \frac{π}{240} + \frac{πn}{60}

t = \frac{π}{240} + \frac{πn}{60}

Solve

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

120 t = \frac{3 π}{2} + 2 πn

Divide both sides by

120

120 t = \frac{3 π}{2} + 2 πn

Divide both sides by

120

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

Simplify

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

Simplify

\frac{120 t}{120} : t

\frac{120 t}{120}

Divide the numbers:

\frac{120}{120} = 1

= t

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}

t = \frac{π}{80} + \frac{πn}{60}

t = \frac{π}{80} + \frac{πn}{60}

t = \frac{π}{80} + \frac{πn}{60}

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

Popular Examples

sqrt((3\sqrt{3))/pi}=sec(c)

\frac{3 3}{π} = sec (c)

2*sin^2(x)=sin(x)

2 \cdot sin^{2} (x) = sin (x)

sqrt(tan(x))=sqrt(1/3)

tan (x) = \frac{1}{3}

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

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

solvefor a,y=sin(a)solve for

a, y = sin (a)

Frequently Asked Questions (FAQ)

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