Find Amplitude, Period, and Phase Shift y=1/6sin(x/4)

$y = \frac{1}{6} \sin (\frac{x}{4})$

Use the form $a \sin (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = \frac{1}{6}$

$b = \frac{1}{4}$

$c = 0$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $\frac{1}{6}$

Find the period of $\frac{\sin (\frac{x}{4})}{6}$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ in the formula for period.

$\frac{2 π}{| \frac{1}{4} |}$

$\frac{1}{4}$ is approximately $0.25$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 4$

Multiply $4$ by $2$ .

$8 π$

Find the phase shift using the formula $\frac{c}{b}$ .

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The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{0}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $0 \cdot 4$

Multiply $0$ by $4$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $\frac{1}{6}$

Period: $8 π$

Phase Shift: None

Vertical Shift: None

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Name

Name	one billion four hundred seventy-one million thirty-seven thousand six hundred sixteen

Interesting facts

1471037616 has 128 divisors, whose sum is 8347905360
The reverse of 1471037616 is 6167301741
Previous prime number is 113

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 36
Digital Root 9

Name

Name	one billion eighty-five million four hundred one thousand eighty-five

Interesting facts

1085401085 has 8 divisors, whose sum is 1302664920
The reverse of 1085401085 is 5801045801
Previous prime number is 11173

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 32
Digital Root 5

Name

Name	one hundred fourteen million four hundred eighty-four thousand eight hundred forty-two

Interesting facts

114484842 has 16 divisors, whose sum is 200851200
The reverse of 114484842 is 248484411
Previous prime number is 19

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

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