# Graph f(t)=3sin(4t)

Graph f(t)=3sin(4t)
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.
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 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:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
Select a few points to graph.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
Multiply by .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
List the points in a table.
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name one billion nine hundred sixty-six million four hundred ninety-nine thousand four hundred fifty

### Interesting facts

• 1966499450 has 16 divisors, whose sum is 3094896168
• The reverse of 1966499450 is 0549946691
• Previous prime number is 113

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 53
• Digital Root 8

### Name

Name five hundred seventeen million twenty-one thousand four hundred sixty-six

### Interesting facts

• 517021466 has 32 divisors, whose sum is 853847568
• The reverse of 517021466 is 664120715
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 32
• Digital Root 5

### Name

Name two hundred fifty-nine million nine hundred fifty-six thousand seven hundred sixty-four

### Interesting facts

• 259956764 has 32 divisors, whose sum is 611059680
• The reverse of 259956764 is 467659952
• Previous prime number is 1669

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 53
• Digital Root 8