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

$y = - \cos (- x + π)$

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

$a = - 1$

$b = - 1$

$c = - π$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

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

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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 $- 1$ and $0$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

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: $\frac{- π}{- 1}$

Dividing two negative values results in a positive value.

Phase Shift: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: None

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Name

Name	two hundred thirty-one million four hundred ten thousand seven hundred eighty-two

Interesting facts

231410782 has 8 divisors, whose sum is 347184936
The reverse of 231410782 is 287014132
Previous prime number is 7507

Basic properties

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

Name

Name	one billion five hundred seventy-six million six hundred thirty-eight thousand two hundred ninety-seven

Interesting facts

1576638297 has 16 divisors, whose sum is 1692979200
The reverse of 1576638297 is 7928366751
Previous prime number is 59

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 54
Digital Root 9

Name

Name	one billion nine hundred seventy-nine million one hundred sixty-seven thousand nine hundred sixty-two

Interesting facts

1979167962 has 16 divisors, whose sum is 4065318432
The reverse of 1979167962 is 2697619791
Previous prime number is 37

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 57
Digital Root 3

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