Find Amplitude, Period, and Phase Shift y=1/7sin(6x)-3

$y = \frac{1}{7} \sin (6 x) - 3$

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

$a = \frac{1}{7}$

$b = 6$

$c = 0$

$d = - 3$

Find the amplitude $| a |$ .

Amplitude: $\frac{1}{7}$

Find the period using the formula $\frac{2 π}{| b |}$ .

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Find the period of $\frac{\sin (6 x)}{7}$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $6$ in the formula for period.

$\frac{2 π}{| 6 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$\frac{2 π}{6}$

Cancel the common factor of $2$ and $6$ .

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Factor $2$ out of $2 π$ .

$\frac{2 (π)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$\frac{2 π}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 π}{2 \cdot 3}$

Rewrite the expression.

$\frac{π}{3}$

Find the period of $- 3$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $6$ in the formula for period.

$\frac{2 π}{| 6 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$\frac{2 π}{6}$

Cancel the common factor of $2$ and $6$ .

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Factor $2$ out of $2 π$ .

$\frac{2 (π)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$\frac{2 π}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 π}{2 \cdot 3}$

Rewrite the expression.

$\frac{π}{3}$

The period of addition/subtraction of trig functions is the maximum of the individual periods.

$\frac{π}{3}$

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: $\frac{0}{6}$

Divide $0$ by $6$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $\frac{1}{7}$

Period: $\frac{π}{3}$

Phase Shift: None

Vertical Shift: $- 3$

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Name

Name	one billion six hundred eighty-eight million six hundred forty-four thousand fifty-seven

Interesting facts

1688644057 has 8 divisors, whose sum is 1779377600
The reverse of 1688644057 is 7504468861
Previous prime number is 967

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	seven hundred forty-six million six hundred sixty thousand five hundred ninety-three

Interesting facts

746660593 has 8 divisors, whose sum is 882751680
The reverse of 746660593 is 395066647
Previous prime number is 29

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 46
Digital Root 1

Name

Name	one billion eight hundred eighty-four million six hundred forty-four thousand eight hundred ninety-three

Interesting facts

1884644893 has 4 divisors, whose sum is 1928473888
The reverse of 1884644893 is 3984464881
Previous prime number is 43

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 55
Digital Root 1

Graph v=11i+11j

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