Question

Write an
equation of the cosine function with amplitude 3 and period 81.

Answer 1

y = 3cos(81x)

Explanation:

Hello!

Here is the foundational equation to find sine and cosine:

y = A sin(B(x + C)) + D

Any cosine function can be written as a sine function. y = A sin(Bx) and y = A cos(Bx). The number, A, in front of sine or cosine changes the height of the graph. The value A (in front of sin or cos) affects the amplitude (height). B is the period by which the width of the wavelengths are measrured. C is known as the phase shift, which is positive to the left on graph. D is the vertical shift of function.

The amplitude changes the heaight of the cosine function by 3 units. The period is indicated as 81 and , but usually we must first use the equation that is the usual given: period =
`(2\pi )/(|B|)` . B must always have an absolute sign to have a psotive value. In this case, the period was given to us.

So, the final equation looks like this:

y = 3cos(81x)

Hope this helps!