Find Amplitude, Period, and Phase Shift y=4cos(3pix+2/5)

$y = 4 \cos (3 π x + \frac{2}{5})$

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

$a = 4$

$b = 3 π$

$c = - \frac{2}{5}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $4$

Find the period of $4 \cos (3 π x + \frac{2}{5})$ .

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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: $\frac{- \frac{2}{5}}{3 π}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $- \frac{2}{5} \cdot \frac{1}{3 π}$

Multiply $- \frac{2}{5} \cdot \frac{1}{3 π}$ .

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Multiply $\frac{1}{3 π}$ and $\frac{2}{5}$ .

Phase Shift: $- \frac{2}{3 π \cdot 5}$

Multiply $5$ by $3$ .

Phase Shift: $- \frac{2}{15 π}$

List the properties of the trigonometric function.

Amplitude: $4$

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

Phase Shift: $- \frac{2}{15 π}$ ( $\frac{2}{15 π}$ to the left)

Vertical Shift: None

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Name

Name	forty million seven hundred forty-one thousand seven hundred sixty-eight

Interesting facts

40741768 has 16 divisors, whose sum is 137503494
The reverse of 40741768 is 86714704
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 37
Digital Root 1

Name

Name	four hundred thirty-eight million one hundred fifty-nine thousand two hundred seventy

Interesting facts

438159270 has 16 divisors, whose sum is 797168880
The reverse of 438159270 is 072951834
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 39
Digital Root 3

Name

Name	one billion four hundred forty-seven million six hundred forty-two thousand four hundred sixty-one

Interesting facts

1447642461 has 8 divisors, whose sum is 1932384384
The reverse of 1447642461 is 1642467441
Previous prime number is 881

Basic properties

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

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Find the Quadrant of the Angle 54 degrees

Solve the Triangle tri{4}{}{4}{}{2}{}

Convert to a Simplified Fraction square root of 64