Find Amplitude, Period, and Phase Shift y=sin(1/6(x+pi/3))

$y = \sin (\frac{1}{6} (x + \frac{π}{3}))$

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

$a = 1$

$b = \frac{1}{6}$

$c = - \frac{π}{18}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

Find the period of $\sin (\frac{x}{6} + \frac{π}{18})$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{6}$ in the formula for period.

$\frac{2 π}{| \frac{1}{6} |}$

$\frac{1}{6}$ is approximately $0.1\overline{6}$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{6}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 6$

Multiply $6$ by $2$ .

$12 π$

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: $\frac{- \frac{π}{18}}{\frac{1}{6}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $- \frac{π}{18} \cdot 6$

Cancel the common factor of $6$ .

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Move the leading negative in $- \frac{π}{18}$ into the numerator.

Phase Shift: $\frac{- π}{18} \cdot 6$

Factor $6$ out of $18$ .

Phase Shift: $\frac{- π}{6 (3)} \cdot 6$

Cancel the common factor.

Phase Shift: $\frac{- π}{6 \cdot 3} \cdot 6$

Rewrite the expression.

Phase Shift: $\frac{- π}{3}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{π}{3}$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $12 π$

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

Vertical Shift: None

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Name

Name	one hundred thirty-eight million three hundred fourteen thousand eight hundred twenty

Interesting facts

138314820 has 32 divisors, whose sum is 391234536
The reverse of 138314820 is 028413831
Previous prime number is 21

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 30
Digital Root 3

Name

Name	one billion two hundred ten million seven hundred seventeen thousand four hundred nineteen

Interesting facts

1210717419 has 4 divisors, whose sum is 1614289896
The reverse of 1210717419 is 9147170121
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 33
Digital Root 6

Name

Name	two billion seventy-three million two hundred sixty-two thousand one hundred sixty-eight

Interesting facts

2073262168 has 32 divisors, whose sum is 6998651424
The reverse of 2073262168 is 8612623702
Previous prime number is 5647

Basic properties

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

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