Find Amplitude, Period, and Phase Shift y=4sin((8x)/5-pi/2)

$y = 4 \sin (\frac{8 x}{5} - \frac{π}{2})$

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

$a = 4$

$b = \frac{8}{5}$

$c = \frac{π}{2}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $4$

Find the period of $4 \sin (\frac{8 x}{5} - \frac{π}{2})$ .

Tap for more steps...

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{8}{5}$ in the formula for period.

$\frac{2 π}{| \frac{8}{5} |}$

$\frac{8}{5}$ is approximately $1.6$ which is positive so remove the absolute value

$\frac{2 π}{\frac{8}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \frac{5}{8}$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $2 π$ .

$2 (π) \frac{5}{8}$

Factor $2$ out of $8$ .

$2 (π) \frac{5}{2 (4)}$

Cancel the common factor.

$2 π \frac{5}{2 \cdot 4}$

Rewrite the expression.

$π \frac{5}{4}$

Combine $π$ and $\frac{5}{4}$ .

$\frac{π \cdot 5}{4}$

Move $5$ to the left of $π$ .

$\frac{5 π}{4}$

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: $\frac{\frac{π}{2}}{\frac{8}{5}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{π}{2} \cdot \frac{5}{8}$

Multiply $\frac{π}{2} \cdot \frac{5}{8}$ .

Tap for more steps...

Multiply $\frac{π}{2}$ and $\frac{5}{8}$ .

Phase Shift: $\frac{π \cdot 5}{2 \cdot 8}$

Multiply $2$ by $8$ .

Phase Shift: $\frac{π \cdot 5}{16}$

Move $5$ to the left of $π$ .

Phase Shift: $\frac{5 π}{16}$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $\frac{5 π}{4}$

Phase Shift: $\frac{5 π}{16}$ ( $\frac{5 π}{16}$ to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=4sin((8x)/5-pi/2)? 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	one billion seven hundred seventy-three million nine hundred fifty-nine thousand two hundred eighty-eight

Interesting facts

1773959288 has 32 divisors, whose sum is 5989691448
The reverse of 1773959288 is 8829593771
Previous prime number is 2381

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 59
Digital Root 5

Name

Name	two billion eighteen million eight hundred eighty-three thousand three hundred sixty-three

Interesting facts

2018883363 has 8 divisors, whose sum is 2115871296
The reverse of 2018883363 is 3633888102
Previous prime number is 2671

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	one billion four hundred fifty-four million seven hundred sixty-one thousand eight hundred forty-one

Interesting facts

1454761841 has 8 divisors, whose sum is 1566969600
The reverse of 1454761841 is 1481674541
Previous prime number is 13099

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

Convert to Polar Coordinates (5,135)

Evaluate square root of 5.49

Convert from Radians to Degrees 210

Graph (1/6)*360

Find the Exact Value sin((2pi)/2)