Take a look at the applet: Cosine function
Above you see the graph of with in radians on . The solutions of are shown ( is a constant).
The solution of within is arccosine of c: .
There (often) is another solution within a range of one period.
Due to the symmetry of the graph that other solution is .
Because of the period of all solutions of are given by:
where k is any integer.
The equation only has solutions if .
The graph of the cosine function strongly resembles the graph of the sine function. Therefore there are several relations between the two.
Take a look at the applet: Unit circle
The graph of with in radians, the standard cosine graph strongly resembles the standard sine graph and the period also is . It has only been shifted to the left by 1/2Π.
This means that .
Furthermore, it is possible to draw the sine and cosine of the same angle in one unit
circle. When you do this, you see that the coördinates op point can be written as: and .
Using Pythagoras' theorem you can check that:
To decrease the number of brackets you can use:
There are some values that are easy to use:
and vice versa:
Use these values, when exact answers are required.