what is an equation for a sine curve with amplitude 2, and period 4pi radians?
Sure, here's a "sine-sational" equation for you:
y = 2sin(x/2)
Just remember, when it comes to equations, it's all about finding the right "sine" language!
To find an equation for a sine curve with an amplitude of 2 and a period of 4π radians, you can use the general equation for a sine function:
y = A*sin(Bx + C)
Where:
A = Amplitude
B = Frequency
C = Phase Shift
In this case, the given amplitude is 2, which means A = 2. The period of 4π radians tells us that the entire cycle of the sine curve repeats every 4π radians. Since the period is determined by the frequency B, we can use the formula:
Period = 2π / B
Since the given period is 4π radians, we can set up the equation:
4π = 2π / B
Simplifying this equation, we get:
B = 1/2
Now we know that B = 1/2, and we can substitute the values of A and B into the equation to get the final equation:
y = 2*sin((1/2)x + C)
The phase shift, C, is not specified in the given information. If you have additional information regarding the phase shift, you can substitute that value too.
To find an equation for a sine curve with a given amplitude and period, you can use the following form:
y = A * sin(Bx)
Where:
- A represents the amplitude of the sine curve.
- B relates to the period of the curve through the formula B = 2π / Period.
In this case, the given amplitude is 2, and the period is 4π radians. Let's substitute these values into the equation:
Amplitude: A = 2
Period: 4π radians
Finding B:
B = 2π / Period
B = 2π / 4π
B = 1/2
Now we can write the equation:
y = 2 * sin((1/2)x)
Therefore, the equation for a sine curve with an amplitude of 2 and a period of 4π radians is y = 2 * sin((1/2)x).
you know that sin(x) has period 2pi. So, since x/2 changes half as fast, it has period 4pi:
y = 2sin(x/2)