Evaluating Trigonometry For Special Angles

We will first look into the trigonometric functions of the special angles 30˚, 45˚ and 60˚.

Let us consider 30˚ and 60˚.

These two angles form a 30˚-60˚-90˚ right triangle as shown.

The ratio of the sides of the triangle is

From the triangle we get the ratios as follows:

Next, we consider the 45˚ angle that forms a 45˚-45˚-90˚ right triangle as shown. The ratio of the sides of the triangle is

From the triangle we get the ratios as follows:

Combining the two tables we get:

Example:

Evaluate the following without using a calculator:

a) 2 sin 30˚ + 3 cos 60˚ – 3 tan 45˚

b) 3(cos 30˚) 2 + 2 sin 30˚

Solution:

a) 2 sin 30˚ + 3 cos 60˚ – 3 tan 45˚

b) 3(cos 30˚) 2 + 2 (sin 30˚) 2

The following video explains how the trigonometry values for the special angles are obtained:

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