What is the general solution for 100=100+30sin((12pi)/5 t) ?

The general solution for 100=100+30sin((12pi)/5 t) is t=(5n)/6 ,t= 5/12+(5n)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

100=100+30sin((12pi)/5 t)

Solution

100 = 100 + 30 sin (\frac{12 π}{5} t)

Solution

t = \frac{5 n}{6}, t = \frac{5}{12} + \frac{5 n}{6}

Degrees

t = 0^{\circ} + 47.74648 \dots^{\circ} n, t = 23.87324 \dots^{\circ} + 47.74648 \dots^{\circ} n

Solution steps

100 = 100 + 30 sin (\frac{12 π}{5} t)

Switch sides

100 + 30 sin (\frac{12 π}{5} t) = 100

Subtract

100

from both sides

100 + 30 sin (\frac{12 π}{5} t) - 100 = 100 - 100

Simplify

30 sin (\frac{12 π}{5} t) = 0

Divide both sides by

30

30 sin (\frac{12 π}{5} t) = 0

Divide both sides by

30

\frac{30 sin ( \frac{12 π}{5} t )}{30} = \frac{0}{30}

Simplify

sin (\frac{12 π}{5} t) = 0

sin (\frac{12 π}{5} t) = 0

General solutions for

sin (\frac{12 π}{5} t) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{12 π}{5} t = 0 + 2 πn, \frac{12 π}{5} t = π + 2 πn

\frac{12 π}{5} t = 0 + 2 πn, \frac{12 π}{5} t = π + 2 πn

Solve

\frac{12 π}{5} t = 0 + 2 πn : t = \frac{5 n}{6}

\frac{12 π}{5} t = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{12 π}{5} t = 2 πn

Multiply both sides by

5

\frac{12 π}{5} t = 2 πn

Multiply both sides by

5

5 \cdot \frac{12 π}{5} t = 5 \cdot 2 πn

Simplify

12 π t = 10 πn

12 π t = 10 πn

Divide both sides by

12 π

12 π t = 10 πn

Divide both sides by

12 π

\frac{12 π t}{12 π} = \frac{10 πn}{12 π}

Simplify

\frac{12 π t}{12 π} = \frac{10 πn}{12 π}

Simplify

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

Divide the numbers:

\frac{12}{12} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Cancel the common factor:

2

= \frac{5 πn}{6 π}

Cancel the common factor:

π

= \frac{5 n}{6}

t = \frac{5 n}{6}

t = \frac{5 n}{6}

t = \frac{5 n}{6}

Solve

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

\frac{12 π}{5} t = π + 2 πn

Multiply both sides by

5

\frac{12 π}{5} t = π + 2 πn

Multiply both sides by

5

5 \cdot \frac{12 π}{5} t = 5 π + 5 \cdot 2 πn

Simplify

12 π t = 5 π + 10 πn

12 π t = 5 π + 10 πn

Divide both sides by

12 π

12 π t = 5 π + 10 πn

Divide both sides by

12 π

\frac{12 π t}{12 π} = \frac{5 π}{12 π} + \frac{10 πn}{12 π}

Simplify

\frac{12 π t}{12 π} = \frac{5 π}{12 π} + \frac{10 πn}{12 π}

Simplify

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

Divide the numbers:

\frac{12}{12} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{5 π}{12 π} + \frac{10 πn}{12 π} : \frac{5}{12} + \frac{5 n}{6}

\frac{5 π}{12 π} + \frac{10 πn}{12 π}

Cancel

\frac{5 π}{12 π} : \frac{5}{12}

\frac{5 π}{12 π}

Cancel the common factor:

π

= \frac{5}{12}

= \frac{5}{12} + \frac{10 πn}{12 π}

Cancel

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Cancel

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Cancel the common factor:

2

= \frac{5 πn}{6 π}

Cancel the common factor:

π

= \frac{5 n}{6}

= \frac{5 n}{6}

= \frac{5}{12} + \frac{5 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5 n}{6}, t = \frac{5}{12} + \frac{5 n}{6}

Popular Examples

(10)/(sin(x))=(100)/(sin(90))

\frac{10}{sin ( x )} = \frac{100}{sin ( 9 0 ^{\circ} )}

(sin(120))/(2.34)=(sin(θ))/(1.2)

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

tan(x)= 12/50

tan (x) = \frac{12}{50}

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

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

(cos(x)-1)(cos(x)+1)=0

(cos (x) - 1) (cos (x) + 1) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 100=100+30sin((12pi)/5 t) ?
The general solution for 100=100+30sin((12pi)/5 t) is t=(5n)/6 ,t= 5/12+(5n)/6