How do you write a period with amplitude and cosine?

Posted on by Muna Meyer

How do you write a period with amplitude and cosine?

1 Answer

  1. In y=acos(b(x−c))+d :
  2. • |a| is the amplitude. • 2πb is the period.
  3. The amplitude is 3 , so a=3 .
  4. The period is 2π3 , so we solve for b .
  5. b=3.
  6. The phase shift is +π9 , so c=π9 .
  7. The vertical transformation is +4 , so d=4 .
  8. ∴ The equation is y=3cos(3(x−π9))+4 , which can be written as y=3cos(3x−π3)+4.

How do you find the period of a cosine graph?

Use the form acos(bx−c)+d a cos ( b x – c ) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude |a| . Find the period using the formula 2π|b| 2 π | b | . The period of the function can be calculated using 2π|b| 2 π | b | .

What is period and amplitude?

The Period goes from one peak to the next (or from any point to the next matching point): The Amplitude is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.

What is a period of a sine graph?

The period of the sine curve is the length of one cycle of the curve. 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 sine?

2π
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 cosine?

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis.

What is the period in a cosine graph?

The cosine function is a trigonometric function that’s called periodic. 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 the period for sine and cosine?

2 π
Explanation: The answer is 2 π because the wavelengths in sine and cosine functions repeats every 2 π units.