Cosine

Concept

In this course, we will be looking at the general solutions of cosine ,where k is a constant and -1= k = 1

There is always a value between 0 and such that cosine (-1= k = 1). This value is known as the principal value of ?. is known as the principal solution of . The intersection of the line and the cosine graph shows that are also solutions of cosine .

The general expression of these solutions is given by = , Z

This is called the general solution of cosine

If the solution is required in degrees, then the general solution is , Z

Scholar's Tip: If , the general solution would be , Z

Also, if k < -1 or k > 1, there is no solution for cosine since the graphs do not intersect.

Examples

Find the general solutions to the following cosine equations.

a) cosine b)

We make use of supplementary angles. cosine = - cosine ?

a) cosine

 

b)

cosine

cosine

We have to consider the two different cases.

Case 1 (taking the sign to be positive):

, Z

Case 2 (taking the sign to be negative):

, Z

We hope you have understood the general solutions of cosine.

You may want to look at sine, tangent solutions as well . There is also the law of sines and law of cosines .

Return to Trigonometry Help or Basic Trigonometry .