What is the general solution for 100+60sin((7pi)/3 x)=100,0<= x<= 1 ?

Q: What is the general solution for 100+60sin((7pi)/3 x)=100,0<= x<= 1 ?

The general solution for 100+60sin((7pi)/3 x)=100,0<= x<= 1 is x=0,x= 3/7 ,x= 6/7

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100+60sin((7pi)/3 x)=100,0<= x<= 1

Solution

100 + 60 sin (\frac{7 π}{3} x) = 100, 0 \leq x \leq 1

Solution

x = 0, x = \frac{3}{7}, x = \frac{6}{7}

Degrees

x = 0^{\circ}, x = 24.55533 \dots^{\circ}, x = 49.11066 \dots^{\circ}

Solution steps

100 + 60 sin (\frac{7 π}{3} x) = 100, 0 \leq x \leq 1

Subtract

100

from both sides

100 + 60 sin (\frac{7 π}{3} x) - 100 = 100 - 100

Simplify

60 sin (\frac{7 π}{3} x) = 0

Divide both sides by

60

60 sin (\frac{7 π}{3} x) = 0

Divide both sides by

60

\frac{60 sin ( \frac{7 π}{3} x )}{60} = \frac{0}{60}

Simplify

sin (\frac{7 π}{3} x) = 0

sin (\frac{7 π}{3} x) = 0

General solutions for

sin (\frac{7 π}{3} x) = 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{7 π}{3} x = 0 + 2 πn, \frac{7 π}{3} x = π + 2 πn

\frac{7 π}{3} x = 0 + 2 πn, \frac{7 π}{3} x = π + 2 πn

Solve

\frac{7 π}{3} x = 0 + 2 πn : x = \frac{6 n}{7}

\frac{7 π}{3} x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{7 π}{3} x = 2 πn

Multiply both sides by

3

\frac{7 π}{3} x = 2 πn

Multiply both sides by

3

3 \cdot \frac{7 π}{3} x = 3 \cdot 2 πn

Simplify

7 π x = 6 πn

7 π x = 6 πn

Divide both sides by

7 π

7 π x = 6 πn

Divide both sides by

7 π

\frac{7 π x}{7 π} = \frac{6 πn}{7 π}

Simplify

x = \frac{6 n}{7}

x = \frac{6 n}{7}

Solve

\frac{7 π}{3} x = π + 2 πn : x = \frac{3}{7} + \frac{6 n}{7}

\frac{7 π}{3} x = π + 2 πn

Multiply both sides by

3

\frac{7 π}{3} x = π + 2 πn

Multiply both sides by

3

3 \cdot \frac{7 π}{3} x = 3 π + 3 \cdot 2 πn

Simplify

7 π x = 3 π + 6 πn

7 π x = 3 π + 6 πn

Divide both sides by

7 π

7 π x = 3 π + 6 πn

Divide both sides by

7 π

\frac{7 π x}{7 π} = \frac{3 π}{7 π} + \frac{6 πn}{7 π}

Simplify

\frac{7 π x}{7 π} = \frac{3 π}{7 π} + \frac{6 πn}{7 π}

Simplify

\frac{7 π x}{7 π} : x

\frac{7 π x}{7 π}

Divide the numbers:

\frac{7}{7} = 1

= \frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{3 π}{7 π} + \frac{6 πn}{7 π} : \frac{3}{7} + \frac{6 n}{7}

\frac{3 π}{7 π} + \frac{6 πn}{7 π}

Cancel

\frac{3 π}{7 π} : \frac{3}{7}

\frac{3 π}{7 π}

Cancel the common factor:

π

= \frac{3}{7}

= \frac{3}{7} + \frac{6 πn}{7 π}

Cancel

\frac{6 πn}{7 π} : \frac{6 n}{7}

\frac{6 πn}{7 π}

Cancel the common factor:

π

= \frac{6 n}{7}

= \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{6 n}{7}, x = \frac{3}{7} + \frac{6 n}{7}

Solutions for the range

0 \leq x \leq 1

x = 0, x = \frac{3}{7}, x = \frac{6}{7}

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Frequently Asked Questions (FAQ)

What is the general solution for 100+60sin((7pi)/3 x)=100,0<= x<= 1 ?
The general solution for 100+60sin((7pi)/3 x)=100,0<= x<= 1 is x=0,x= 3/7 ,x= 6/7