Find Amplitude, Period, and Phase Shift y=1/2cos((4pix)/5-5pi)

Find Amplitude, Period, and Phase Shift y=1/2cos((4pix)/5-5pi)
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
Factor out of .
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Combine and .
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift: None
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Name

Name one billion three hundred fifteen million two hundred fifty thousand nine hundred seventy-nine

Interesting facts

• 1315250979 has 16 divisors, whose sum is 2008554240
• The reverse of 1315250979 is 9790525131
• Previous prime number is 461

Basic properties

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

Name

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

Interesting facts

• 1542553845 has 8 divisors, whose sum is 1558057536
• The reverse of 1542553845 is 5483552451
• Previous prime number is 3863

Basic properties

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

Name

Name one billion nine hundred fifteen million seven hundred eighty-seven thousand eight hundred fourteen

Interesting facts

• 1915787814 has 32 divisors, whose sum is 3864261600
• The reverse of 1915787814 is 4187875191
• Previous prime number is 397

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 51
• Digital Root 6