Find Amplitude, Period, and Phase Shift y=1/4cos(3pix)

$y = \frac{1}{4} \cos (3 π x)$

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

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

$b = 3 π$

$c = 0$

$d = 0$

Find the amplitude $| a |$ .

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

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

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

$\frac{2 π}{| b |}$

Replace $b$ with $3 π$ in the formula for period.

$\frac{2 π}{| 3 π |}$

$3 π$ is approximately $9.42477796$ which is positive so remove the absolute value

$\frac{2 π}{3 π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{2 π}{3 π}$

Rewrite the expression.

$\frac{2}{3}$

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: $\frac{0}{3 π}$

Cancel the common factor of $0$ and $3$ .

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Factor $3$ out of $0$ .

Phase Shift: $\frac{3 (0)}{3 π}$

Cancel the common factors.

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Factor $3$ out of $3 π$ .

Phase Shift: $\frac{3 (0)}{3 (π)}$

Cancel the common factor.

Phase Shift: $\frac{3 \cdot 0}{3 π}$

Rewrite the expression.

Phase Shift: $\frac{0}{π}$

Divide $0$ by $π$ .

Phase Shift: $0$

List the properties of the trigonometric function.

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

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

Phase Shift: None

Vertical Shift: None

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Name

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

Interesting facts

1779132360 has 128 divisors, whose sum is 9811756800
The reverse of 1779132360 is 0632319771
Previous prime number is 47

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	seven hundred twenty-nine million nine hundred forty-nine thousand six hundred eighteen

Interesting facts

729949618 has 4 divisors, whose sum is 1094924430
The reverse of 729949618 is 816949927
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 55
Digital Root 1

Name

Name	two billion one hundred fifteen million seven hundred forty-nine thousand five hundred

Interesting facts

2115749500 has 64 divisors, whose sum is 5947512480
The reverse of 2115749500 is 0059475112
Previous prime number is 1259

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 34
Digital Root 7

Expand the Logarithmic Expression log base b of ninth root of (x^4)/(y^9x^5)

Find the Reference Angle -580 degrees

Graph cot(111)

Graph 3sec(1/7x)

Solve the Triangle C=30 , A=89 , b=7