Trigonometry/Graphs of Sine and Cosine Functions

From Wikibooks, open books for an open world
Jump to: navigation, search

The graph of the sine function looks like this:

Graph of the sine function

Careful analysis of this graph will show that the graph corresponds to the unit circle. X is essentially the degree measure (in radians), while Y is the value of the sine function.

The graph of the cosine function looks like this:

Graph of the cosine function

As with the sine function, analysis of the cosine function will show that the graph corresponds to the unit circle. One of the most important differences between the sine and cosine functions is that sine is an odd function (i.e. sin(-θ) = -sin θ) while cosine is an even function (i.e. cos(-θ) = cos θ).

Sine and cosine are periodic functions; that is, the above is repeated for preceding and following intervals with length 2π.

Sine and cosine on same graph


Exercises[edit]

When does Sine = Cosine?

For what value of \displaystyle\theta does \displaystyle \sin \theta=\cos\theta? (Choose a value between 0 and 90o or equivalently in radians between 0 and \displaystyle \frac{\pi}{2}).

  • Convince yourself you are right by drawing the triangle and using SOH-CAH-TOA.