Cosine Function Graph Math

Calculate the graph s maximum and.

Cosine function graph math. In these lessons we will look at graphing the cosine function and properties of the cosine function. We start with the graph of the basic sine function y sin x and the basic cosine function g x cos x we then present examples of how to graph transformed versions of these same functions. Graphing the cosine function one period of a trigonometric function is from 0 to 360 degrees. The graphs of the sine and cosine functions illustrate a property that exists for several pairings of the different trig functions.

In both graphs the shape of the graph repeats after 2π which means the functions are periodic with a period of 2π. Use the basic equations as given y sin x displaystyle y sin x andy c o s x displaystyle y cos x for a sine or cosine graph simply go from 0 to 2π on the x axis and 1 to 1 on the y axis intersecting at the origin. The graph of the cosine is the darker curve. Note how it s shifted to the left of the sine curve.

Therefore 0 to 2π would be one period. Here we will use radians. The result as seen above is a smooth curve that varies from 1 to 1. The graphs of y sin x and y cos x on the same axes.

Graphs of the sine and the cosine functions of the form y a sin b x c d and y a cos b x c d are discussed with several examples including detailed solutions. However radian measurement is typically used to graph a trigonometric function. Plot of sine and cosine in fact sine and cosine are like good friends. Graphing cosine function the trigonometric ratios can also be considered as functions of a variable which is the measure of an angle.

To graph the cosine function we mark the angle along the horizontal x axis and for each angle we put the cosine of that angle on the vertical y axis. A unit circle is a circle of radius one unit with its center at the origin. By thinking of the sine and cosine values as coordinates of points on a unit circle it becomes clear that the range of both functions must be the interval 1 1. They follow each other exactly π 2 radians 90 apart.

The following diagram shows the unit circle and the cosine graph. Like with sine graphs the domain of cosine is all real numbers and its range is calculate the graph s x intercepts. Here are the steps. Both y sin x displaystyle y sin x and y cos.

This angle measure can either be given in degrees or radians. We will start with the unit circle. Find the values for domain and range.