Find Amplitude, Period, and Phase Shift y=2cos((8x)/3-2pi)

$y = 2 \cos (\frac{8 x}{3} - 2 π)$

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

$a = 2$

$b = \frac{8}{3}$

$c = 2 π$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $2$

Find the period of $2 \cos (\frac{8 x}{3} - 2 π)$ .

Tap for more steps...

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{8}{3}$ in the formula for period.

$\frac{2 π}{| \frac{8}{3} |}$

$\frac{8}{3}$ is approximately $2.\overline{6}$ which is positive so remove the absolute value

$\frac{2 π}{\frac{8}{3}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \frac{3}{8}$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $2 π$ .

$2 (π) \frac{3}{8}$

Factor $2$ out of $8$ .

$2 (π) \frac{3}{2 (4)}$

Cancel the common factor.

$2 π \frac{3}{2 \cdot 4}$

Rewrite the expression.

$π \frac{3}{4}$

Combine $π$ and $\frac{3}{4}$ .

$\frac{π \cdot 3}{4}$

Move $3$ to the left of $π$ .

$\frac{3 π}{4}$

Find the phase shift using the formula $\frac{c}{b}$ .

Tap for more steps...

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: $\frac{2 π}{\frac{8}{3}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $2 π (\frac{3}{8})$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $2 π$ .

Phase Shift: $2 (π) (\frac{3}{8})$

Factor $2$ out of $8$ .

Phase Shift: $2 (π) (\frac{3}{2 (4)})$

Cancel the common factor.

Phase Shift: $2 π (\frac{3}{2 \cdot 4})$

Rewrite the expression.

Phase Shift: $π (\frac{3}{4})$

Combine $π$ and $\frac{3}{4}$ .

Phase Shift: $\frac{π \cdot 3}{4}$

Move $3$ to the left of $π$ .

Phase Shift: $\frac{3 π}{4}$

List the properties of the trigonometric function.

Amplitude: $2$

Period: $\frac{3 π}{4}$

Phase Shift: $\frac{3 π}{4}$ ( $\frac{3 π}{4}$ to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=2cos((8x)/3-2pi)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	two hundred fifty million three hundred fifty-four thousand eight hundred twenty-seven

Interesting facts

250354827 has 8 divisors, whose sum is 370896080
The reverse of 250354827 is 728453052
Previous prime number is 9

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	two billion one hundred forty-five million eight hundred ninety-four thousand three hundred fifty-eight

Interesting facts

2145894358 has 16 divisors, whose sum is 3268520640
The reverse of 2145894358 is 8534985412
Previous prime number is 3739

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	seven hundred twelve million five hundred eighty-four thousand eight hundred sixty-three

Interesting facts

712584863 has 8 divisors, whose sum is 730663296
The reverse of 712584863 is 368485217
Previous prime number is 43

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 44
Digital Root 8

Find the Quadrant of the Angle 70.9 degrees

Find Trig Functions Using Identities csc(x)=5/3 , tan(x)=3/4

Solve for x (2x)/7=1/3

Graph y=sin(x+90)+2

Find the Other Trig Values in Quadrant I sec(x)=12