Sine

Concept

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

There is always a value between and such that sine . This value is known as the principal value of ?. is known as the principal solution of

sine . The intersection of the line and the sine graph shows that are also solutions of sine .

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

This is called the general solution of sine

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

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

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

Examples

Find the general solutions to each of the following sine equations.

a) sine b) sine

a) First, we place into its equivalent form in sine function.

sine = sine

solution of img/sine, Z (expressed in radians)

b) sine

, Z (expressed in degrees)

It's good to know the numerical values for the common sine functions.

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

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