What is the general solution for 100=100+40sin((9pi)/4 t) ?

The general solution for 100=100+40sin((9pi)/4 t) is t=(8n)/9 ,t= 4/9+(8n)/9

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100=100+40sin((9pi)/4 t)

Solution

100 = 100 + 40 sin (\frac{9 π}{4} t)

Solution

t = \frac{8 n}{9}, t = \frac{4}{9} + \frac{8 n}{9}

Degrees

t = 0^{\circ} + 50.92958 \dots^{\circ} n, t = 25.46479 \dots^{\circ} + 50.92958 \dots^{\circ} n

Solution steps

100 = 100 + 40 sin (\frac{9 π}{4} t)

Switch sides

100 + 40 sin (\frac{9 π}{4} t) = 100

Subtract

100

from both sides

100 + 40 sin (\frac{9 π}{4} t) - 100 = 100 - 100

Simplify

40 sin (\frac{9 π}{4} t) = 0

Divide both sides by

40

40 sin (\frac{9 π}{4} t) = 0

Divide both sides by

40

\frac{40 sin ( \frac{9 π}{4} t )}{40} = \frac{0}{40}

Simplify

sin (\frac{9 π}{4} t) = 0

sin (\frac{9 π}{4} t) = 0

General solutions for

sin (\frac{9 π}{4} 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{9 π}{4} t = 0 + 2 πn, \frac{9 π}{4} t = π + 2 πn

\frac{9 π}{4} t = 0 + 2 πn, \frac{9 π}{4} t = π + 2 πn

Solve

\frac{9 π}{4} t = 0 + 2 πn : t = \frac{8 n}{9}

\frac{9 π}{4} t = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{9 π}{4} t = 2 πn

Multiply both sides by

4

\frac{9 π}{4} t = 2 πn

Multiply both sides by

4

4 \cdot \frac{9 π}{4} t = 4 \cdot 2 πn

Simplify

9 π t = 8 πn

9 π t = 8 πn

Divide both sides by

9 π

9 π t = 8 πn

Divide both sides by

9 π

\frac{9 π t}{9 π} = \frac{8 πn}{9 π}

Simplify

t = \frac{8 n}{9}

t = \frac{8 n}{9}

Solve

\frac{9 π}{4} t = π + 2 πn : t = \frac{4}{9} + \frac{8 n}{9}

\frac{9 π}{4} t = π + 2 πn

Multiply both sides by

4

\frac{9 π}{4} t = π + 2 πn

Multiply both sides by

4

4 \cdot \frac{9 π}{4} t = 4 π + 4 \cdot 2 πn

Simplify

9 π t = 4 π + 8 πn

9 π t = 4 π + 8 πn

Divide both sides by

9 π

9 π t = 4 π + 8 πn

Divide both sides by

9 π

\frac{9 π t}{9 π} = \frac{4 π}{9 π} + \frac{8 πn}{9 π}

Simplify

\frac{9 π t}{9 π} = \frac{4 π}{9 π} + \frac{8 πn}{9 π}

Simplify

\frac{9 π t}{9 π} : t

\frac{9 π t}{9 π}

Divide the numbers:

\frac{9}{9} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{4 π}{9 π} + \frac{8 πn}{9 π} : \frac{4}{9} + \frac{8 n}{9}

\frac{4 π}{9 π} + \frac{8 πn}{9 π}

Cancel

\frac{4 π}{9 π} : \frac{4}{9}

\frac{4 π}{9 π}

Cancel the common factor:

π

= \frac{4}{9}

= \frac{4}{9} + \frac{8 πn}{9 π}

Cancel

\frac{8 πn}{9 π} : \frac{8 n}{9}

\frac{8 πn}{9 π}

Cancel the common factor:

π

= \frac{8 n}{9}

= \frac{4}{9} + \frac{8 n}{9}

t = \frac{4}{9} + \frac{8 n}{9}

t = \frac{4}{9} + \frac{8 n}{9}

t = \frac{4}{9} + \frac{8 n}{9}

t = \frac{8 n}{9}, t = \frac{4}{9} + \frac{8 n}{9}

Popular Examples

tan(φ)=-1/(sqrt(3))

tan (φ) = - \frac{1}{3}

sin(3m)=0

sin (3 m) = 0

cos(a)=-8/17 ,sin(b)= 3/5

cos (a) = - \frac{8}{17}, sin (b) = \frac{3}{5}

7tan(θ)+9=0

7 tan (θ) + 9 = 0

14=-3.75cos(pi/6 x)+11.25

14 = - 3.75 cos (\frac{π}{6} x) + 11.25

Frequently Asked Questions (FAQ)

What is the general solution for 100=100+40sin((9pi)/4 t) ?
The general solution for 100=100+40sin((9pi)/4 t) is t=(8n)/9 ,t= 4/9+(8n)/9