POINT OF INTEREST 1
NUMERIC VALUES OF THE TRIGONOMETRIC RATIOS OF SPECIAL ANGLES
Copyright by Ingrid Stewart, Ph.D.  Please Send Questions and Comments to ingrid.stewart@csn.edu.

We will derive the numeric values of the six trigonometric ratios of the special angles 30^o, 45^o, 60^o using right triangles and the following definitions.

                   

Let's derive the values of the six trigonometric ratios of the 30^oangle. 

We will use the 30-60-90 triangle. Its sides are in the proportions , where 2c is the length of the hypotenuse of the triangle. 

For simplicity's sake, we will let c = 1, although, c could take on any value and we would still get the same answers!!!

Using the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle 30^o are as follows:

Let's derive the values of the six trigonometric ratios of the 60^o angle.

We will again use the 30-60-90 triangle. 

For simplicity's sake, we will let c = 1, although, c could take on any value and we would still get the same answers!!!

Using the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle 60^o are as follows:

Let's derive the values of the six trigonometric ratios of the 45^o angle.

We will use the 45-45-90 triangle. Its sides are in the proportions , where is the length of the hypotenuse of the triangle. 

For simplicity's sake, we will let c = 1, although, c could take on any value and we would still get the same answers!!!

Using the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle 45^o are as follows: