How do you find the amplitude and period of a sine graph?
Amplitude is the distance between the center line of the function and the top or bottom of the function, and the period is the distance between two peaks of the graph, or the distance it takes for the entire graph to repeat. Using this equation: Amplitude =APeriod =2πBHorizontal shift to the left =CVertical shift =D.
How do you find the period of a sine and cosine graph?
If we have a sine function of the form f(x) = Asin(Bx + C) + D, then the period of the function is 2π / |B|.
How do you find the period and amplitude of an equation?
Finding the amplitude, period, and phase shift of a function of the form A × sin(Bx – C) + D or A × cos(Bx – C) + D goes as follows: The amplitude is equal to A ; The period is equal to 2π / B ; and. The phase shift is equal to C / B .
How do you write a period with amplitude and cosine?
1 Answer
- In y=acos(b(x−c))+d :
- • |a| is the amplitude. • 2πb is the period.
- The amplitude is 3 , so a=3 .
- The period is 2π3 , so we solve for b .
- b=3.
- The phase shift is +π9 , so c=π9 .
- The vertical transformation is +4 , so d=4 .
- ∴ The equation is y=3cos(3(x−π9))+4 , which can be written as y=3cos(3x−π3)+4.
What is the period of sine and cosine?
2π
The period of a sinusoid is the length of a complete cycle. For basic sine and cosine functions, the period is 2π.
What is a period in sine graph?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.
What is the period of Cos?
The period of a periodic function is the interval of x-values on which the cycle of the graph that’s repeated in both directions lies. Therefore, in the case of the basic cosine function, f(x) = cos(x), the period is 2π.
What is amplitude and period of Sine and cosine functions?
Amplitude and Period of Sine and Cosine Functions. The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function. Amplitude = | a |. Let b be a real number. The period of y = a sin ( b x ) and y = a cos ( b x ) is given by. Period = 2 π | b |. Example:
What is the amplitude of sin 4 with period 2π?
So amplitude is 1, period is 2π, there is no phase shift or vertical shift: Example: 2 sin (4 (x − 0.5)) + 3 amplitude A = 2 period 2π/B = 2π/4 = π/2
What is the amplitude of Y = a sin (x)?
The amplitude of y = a sin ( x) and y = a cos ( x) represents half the distance between the maximum and minimum values of the function. Let b be a real number. The period of y = a sin ( b x) and y = a cos ( b x) is given by
How do you find the period of a sin 2x graph?
If f (x)= sin(2x) f ( x) = sin ( 2 x), then B= 2 B = 2, so the period is π π and the graph is compressed. If f (x) = sin(x 2) f ( x) = sin ( x 2), then B= 1 2 B = 1 2, so the period is 4π 4 π and the graph is stretched.