Find Amplitude, Period, and Phase Shift f(t)=-2/3*sin(6t)

$f (t) = - \frac{2}{3} \cdot \sin (6 t)$

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

$a = \frac{2}{3}$

$b = 6$

$c = 0$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $\frac{2}{3}$

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

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

Period: $\frac{2 π}{| b |}$

Replace $b$ with $6$ in the formula for period.

Period: $\frac{2 π}{| 6 |}$

Solve the equation.

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The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

Period: $\frac{2 π}{6}$

Cancel the common factor of $2$ and $6$ .

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Factor $2$ out of $2 π$ .

Period: $\frac{2 (π)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

Period: $\frac{2 π}{2 \cdot 3}$

Cancel the common factor.

Period: $\frac{2 π}{2 \cdot 3}$

Rewrite the expression.

Period: $\frac{π}{3}$

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: $\frac{0}{6}$

Divide $0$ by $6$ .

Phase Shift: $0$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: $\frac{2}{3}$

Period: $\frac{π}{3}$

Phase Shift: $0$ ( $0$ to the right)

Vertical Shift: $0$

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Name

Name	one hundred thirty-nine million two hundred seventy-one thousand three hundred nine

Interesting facts

139271309 has 4 divisors, whose sum is 139993116
The reverse of 139271309 is 903172931
Previous prime number is 193

Basic properties

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

Name

Name	one billion one hundred sixty million nine hundred eighty-four thousand six

Interesting facts

1160984006 has 32 divisors, whose sum is 2151186240
The reverse of 1160984006 is 6004890611
Previous prime number is 277

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 35
Digital Root 8

Name

Name	one billion seven hundred sixty-six million twenty-six thousand one hundred ninety-six

Interesting facts

1766026196 has 32 divisors, whose sum is 4367895840
The reverse of 1766026196 is 6916206671
Previous prime number is 131

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 44
Digital Root 8

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