Find Amplitude, Period, and Phase Shift y=1/4sin(x-(2pi)/3)

$y = \frac{1}{4} \sin (x - \frac{2 π}{3})$

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

$a = \frac{1}{4}$

$b = 1$

$c = \frac{2 π}{3}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $\frac{1}{4}$

Find the period of $\frac{\sin (x - \frac{2 π}{3})}{4}$ .

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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 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: $\frac{\frac{2 π}{3}}{1}$

Divide $\frac{2 π}{3}$ by $1$ .

Phase Shift: $\frac{2 π}{3}$

List the properties of the trigonometric function.

Amplitude: $\frac{1}{4}$

Period: $2 π$

Phase Shift: $\frac{2 π}{3}$ ( $\frac{2 π}{3}$ to the right)

Vertical Shift: None

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Name

Name	one billion four hundred seventy-five million four hundred thousand five hundred eighty-nine

Interesting facts

1475400589 has 4 divisors, whose sum is 1484130940
The reverse of 1475400589 is 9850045741
Previous prime number is 169

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 43
Digital Root 7

Name

Name	one billion six hundred twenty million five hundred thirty-four thousand five hundred eighty-seven

Interesting facts

1620534587 has 16 divisors, whose sum is 1922788800
The reverse of 1620534587 is 7854350261
Previous prime number is 29

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

Name

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

Interesting facts

1065371207 has 4 divisors, whose sum is 1077341760
The reverse of 1065371207 is 7021735601
Previous prime number is 89

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 32
Digital Root 5

Find the Inverse (1+cot(a))/(csc(a))

Find the Exact Value csc((15pi)/8)

Solve for ? cot(x)=3/4

Convert from Radians to Degrees -(5pi)/3

Graph y>-9