Menemukan amplitudo dan periode

Equations of Cosine Functions

The cosine function is a type of periodic function that has both an amplitude and a period. Remember that amplitude is the distance from the center to the highest or lowest point of the graph. The period is the distance between two respective points on a wave.

The equation for a cosine function is: $y=(a)cos(bx)$

Amplitude is represented by $a$. When $b=1$, the period is $2\pi$.

The amplitude of a standard (parent) cosine function is $1$, and the period of a standard (parent) cosine function is $2\pi$.

Equations of the Cosine Function

The standard form of the sine function is:

$$y=a \text{ cos } (x-h) +k$$

Before we dive deeper, though, let's make one clarification. You may remember learning about the Law of Cosines in geometry. This Law was also an equation dealing with cosines, but it was a little different. The Law of Cosines helped you find angles and sides of triangles. If you imagine an angled triangle, you can use the adjacent sides and the opposite side, along with the angle, to find the missing part. You probably learned a similar concept with the Law of Sines.

However, in this lesson, we will focus on trigonometric functions! That means we will look at the cosine function, graphed on a coordinate plan. While this concept can be applied to triangles, triangles are not directly related.

We have seen the standard, parent function before, but we can also apply translations to shift and transform the cosine function! $a$ will change the amplitude, $h$ represents a horizontal shift, and $k$ represents a vertical shift. We've seen a similar concept before with function transformations!

(Video) Find the Amplitude and Period of a Cosine Function

by Brian McLogan

In this video by Brian McLogan, you will learn how to find the amplitude and period of a cosine equation.