Find Amplitude, Period, and Phase Shift y=3sin(100x+1)

$y = 3 \sin (100 x + 1)$

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

$a = 3$

$b = 100$

$c = - 1$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $3$

Find the period of $3 \sin (100 x + 1)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $100$ in the formula for period.

$\frac{2 π}{| 100 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $100$ is $100$ .

$\frac{2 π}{100}$

Cancel the common factor of $2$ and $100$ .

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Factor $2$ out of $2 π$ .

$\frac{2 (π)}{100}$

Cancel the common factors.

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Factor $2$ out of $100$ .

$\frac{2 π}{2 \cdot 50}$

Cancel the common factor.

$\frac{2 π}{2 \cdot 50}$

Rewrite the expression.

$\frac{π}{50}$

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: $\frac{- 1}{100}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{1}{100}$

List the properties of the trigonometric function.

Amplitude: $3$

Period: $\frac{π}{50}$

Phase Shift: $- \frac{1}{100}$ ( $\frac{1}{100}$ to the left)

Vertical Shift: None

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Name

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

Interesting facts

185573566 has 4 divisors, whose sum is 278360352
The reverse of 185573566 is 665375581
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 46
Digital Root 1

Name

Name	one billion five hundred eighty-six million nine hundred eighty-three thousand eight hundred seventy-six

Interesting facts

1586983876 has 32 divisors, whose sum is 3706755048
The reverse of 1586983876 is 6783896851
Previous prime number is 53

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 61
Digital Root 7

Name

Name	seven hundred sixty-two million two hundred nine thousand three hundred six

Interesting facts

762209306 has 4 divisors, whose sum is 1143313962
The reverse of 762209306 is 603902267
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

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