Find Amplitude, Period, and Phase Shift y=6sin(pix-6)-6

$y = 6 \sin (π x - 6) - 6$

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

$a = 6$

$b = π$

$c = 6$

$d = - 6$

Find the amplitude $| a |$ .

Amplitude: $6$

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

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Find the period of $6 \sin (π x - 6)$ .

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

$\frac{2 π}{| b |}$

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

$\frac{2 π}{| π |}$

$π$ is approximately $3.14159265$ which is positive so remove the absolute value

$\frac{2 π}{π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{2 π}{π}$

Divide $2$ by $1$ .

$2$

Find the period of $- 6$ .

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

$\frac{2 π}{| b |}$

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

$\frac{2 π}{| π |}$

$π$ is approximately $3.14159265$ which is positive so remove the absolute value

$\frac{2 π}{π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{2 π}{π}$

Divide $2$ by $1$ .

$2$

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

$2$

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: $\frac{6}{π}$

List the properties of the trigonometric function.

Amplitude: $6$

Period: $2$

Phase Shift: $\frac{6}{π}$ ( $\frac{6}{π}$ to the right)

Vertical Shift: $- 6$

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Name

Name	two billion one million three hundred sixty-nine thousand seven hundred seventeen

Interesting facts

2001369717 has 8 divisors, whose sum is 2225482200
The reverse of 2001369717 is 7179631002
Previous prime number is 1289

Basic properties

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

Name

Name	one billion three hundred seventy-two million five hundred sixty-one thousand seven hundred eighty-six

Interesting facts

1372561786 has 16 divisors, whose sum is 2167968960
The reverse of 1372561786 is 6871652731
Previous prime number is 4231

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 46
Digital Root 1

Name

Name	five hundred forty-one million twenty thousand nine hundred sixty

Interesting facts

541020960 has 256 divisors, whose sum is 5843041920
The reverse of 541020960 is 069020145
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 27
Digital Root 9

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