Find Amplitude, Period, and Phase Shift y=-2cos(x-pi)-2

$y = - 2 \cos (x - π) - 2$

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

$a = - 2$

$b = 1$

$c = π$

$d = - 2$

Find the amplitude $| a |$ .

Amplitude: $2$

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

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Find the period of $- 2 \cos (x - π)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

Find the period of $- 2$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

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

$2 π$

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: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $2$

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $- 2$

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Name

Name	three hundred thirty-five million eleven thousand three hundred eighty-four

Interesting facts

335011384 has 32 divisors, whose sum is 1197173520
The reverse of 335011384 is 483110533
Previous prime number is 17

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 28
Digital Root 1

Name

Name	three hundred three million five hundred seven thousand nine hundred seventy

Interesting facts

303507970 has 32 divisors, whose sum is 579840768
The reverse of 303507970 is 079705303
Previous prime number is 467

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 34
Digital Root 7

Name

Name	eight hundred seventeen million four hundred twenty-five thousand seven hundred ninety-five

Interesting facts

817425795 has 32 divisors, whose sum is 1330536960
The reverse of 817425795 is 597524718
Previous prime number is 1289

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 48
Digital Root 3

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Solve the Triangle a=43 , b=52 , c=60