**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

using right triangles and the following definitions.30^{o}, 45^{o}, 60^{o}

Let's derive the values of the six trigonometric ratios of the

angle.30^{o}We will use the

triangle. Its sides are in the proportions , where30-60-90is the length of the hypotenuse of the triangle.2c

For simplicity's sake, we will let

, although,c = 1could take on any value and we would still get the same answers!!!cUsing the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle

are as follows:30^{o}

Let's derive the values of the six trigonometric ratios of the

angle.60^{o}We will again use the

30-60-90triangle.^{ }

For simplicity's sake, we will let

, although,c = 1could take on any value and we would still get the same answers!!!c

Using the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle

are as follows:60^{o}Let's derive the values of the six trigonometric ratios of the

angle.45^{o}We will use the

45triangle. Its sides are in the proportions , where is the length of the hypotenuse of the triangle.-45-90For simplicity's sake, we will let

, although,c = 1could take on any value and we would still get the same answers!!!cUsing the definition of the trigonometric ratios, please convince yourself that the EXACT values of the six trigonometric ratios of the angle

are as follows:45^{o}