Find Amplitude, Period, and Phase Shift y=5sec(4x)+10

Find Amplitude, Period, and Phase Shift y=5sec(4x)+10
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
Find the period using the formula .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
The period of addition/subtraction of trig functions is the maximum of the individual periods.
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:
Divide by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: None
Vertical Shift:
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Name

Name one billion seven hundred fifty-three million seven hundred sixteen thousand twenty-one

Interesting facts

• 1753716021 has 16 divisors, whose sum is 2347583424
• The reverse of 1753716021 is 1206173571
• Previous prime number is 997

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 33
• Digital Root 6

Name

Name two billion eighty-eight million one hundred ninety-one thousand five hundred forty-five

Interesting facts

• 2088191545 has 8 divisors, whose sum is 2199476160
• The reverse of 2088191545 is 5451918802
• Previous prime number is 29

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 43
• Digital Root 7

Name

Name one billion four hundred thirteen million forty-three thousand three hundred fifty-two

Interesting facts

• 1413043352 has 64 divisors, whose sum is 5583253536
• The reverse of 1413043352 is 2533403141
• Previous prime number is 41

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 26
• Digital Root 8