Find Amplitude, Period, and Phase Shift y=cos(x-pi/3)+2

$y = \cos (x - \frac{π}{3}) + 2$

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

$a = 1$

$b = 1$

$c = \frac{π}{3}$

$d = 2$

Find the amplitude $| a |$ .

Amplitude: $1$

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

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Find the period of $\cos (x - \frac{π}{3})$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $1$ 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: $\frac{\frac{π}{3}}{1}$

Divide $\frac{π}{3}$ by $1$ .

Phase Shift: $\frac{π}{3}$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $2 π$

Phase Shift: $\frac{π}{3}$ ( $\frac{π}{3}$ to the right)

Vertical Shift: $2$

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Name

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

Interesting facts

1405535185 has 4 divisors, whose sum is 1686642228
The reverse of 1405535185 is 5815355041
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 37
Digital Root 1

Name

Name	five hundred fifty-six million two hundred forty-three thousand four hundred twelve

Interesting facts

556243412 has 8 divisors, whose sum is 1251547686
The reverse of 556243412 is 214342655
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 32
Digital Root 5

Name

Name	one billion nine hundred eighty-seven million seven hundred eighty-six thousand seven hundred seventy-seven

Interesting facts

1987786777 has 4 divisors, whose sum is 1987924276
The reverse of 1987786777 is 7776877891
Previous prime number is 16417

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 67
Digital Root 4

Convert from Radians to Degrees -2p

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