Special Angles

Angles with a reference angle of 30^o, 45^o or 60^o are called "special angles" and the exact values of the trig functions can be found, as the following examples illustrate.

Example 5:

Find the exact values of the trig functions of 300^o.

Solution:

We draw the angle in standard position and find that its reference angle is 60^o:

The triangle formed by drawing a perpendicular to the x-axis is a 30-60-90 triangle, so the side opposite the 30 degree angle is half the hypotenuse, so we might as well choose 2 for the length of the hypotenuse, which is our value of r.  Then we have:

Now we can give the exact values of the trig functions:

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