Write a sine function that has an amplitude of 5, a midline of 2 and a period of 7/8
What about amp of 5, midline of 2, and period of 4/7?
Why did the sine function go to acting school?
To learn how to oscillate and create some wave-ty performances!
Alright, let's get brainy and give you the function you're looking for:
f(x) = 5sin(16πx) + 2
Here's the breakdown:
- The amplitude of 5 tells us how high and low the sine function will go.
- The midline of 2 means that the whole function will be shifted up by 2 units.
- The period of 7/8 determines how quickly the function repeats itself. In this case, since the standard period of sin(x) is 2π, we need to alter it to fit a period of 7/8. To do that, we multiply the angle inside the sin by (2π / (7/8)) = (16π).
Hope this brightened up your day, mathematical friendo! If you have any more questions (or jokes), feel free to ask!
To write a sine function with the given amplitude, midline, and period, you can use the general form of the sine function:
f(x) = A sin(B(x - C)) + D
Where:
A = amplitude
B = 2π / period
C = phase shift (horizontal shift)
D = midline (vertical shift)
Given:
Amplitude (A) = 5
Midline (D) = 2
Period = 7/8
1. Substitute the given values into the formula:
f(x) = 5 sin(B(x - C)) + 2
2. Calculate the value of B (2π / period):
B = 2π / (7/8)
B = (2π * 8) / 7
B = (16π) / 7
3. Simplify B:
B ≈ 7.24
4. Rewrite the equation with the calculated values:
f(x) = 5 sin((16π / 7)(x - C)) + 2
Now you have the desired sine function with an amplitude of 5, a midline of 2 and a period of 7/8. Please note that the value of C, which represents the phase shift, was not given in the question, so it is left as a variable in the equation.
To write a sine function with the given amplitude, midline, and period, you can use the general form of the sine function:
y = A sin(Bx + C) + D
Where:
A represents the amplitude.
B affects the period of the function.
C shifts the graph horizontally.
D shifts the graph vertically.
Given:
Amplitude (A) = 5
Midline (D) = 2
Period (T) = 7/8
To find B, you can use the formula:
B = 2π / T
Substituting the given values:
B = 2π / (7/8)
B = 16π / 7
Now we can write the sine function:
y = 5 sin((16π / 7)x + C) + 2
The value of C can be determined based on the phase shift (horizontal shift) of the function. Since no specific phase shift is mentioned, C can be assumed to be zero.
Therefore, the final sine function with an amplitude of 5, a midline of 2, and a period of 7/8 is:
y = 5 sin((16π / 7)x) + 2
sin(kx) has period 2π/k
so, you want
2 + 5sin(16π/7 x)