Lesson 5
Exact Values for Special Angles
Special angles include the quadrantal angles ( 0°, 90° 180°, 270° and 360° ) as well as those from
special right triangles, namely ( 45°, 30° and 60°).
The exact values, if they exist, are found by using intersection points of the unit circle and the x and y axes.
| Unit Circle radius one unit. |  |
Using our definitions of the trig functions in terms of x, y and r we have the following table.
Use your calculator to confirm these values.
Instead of undefined or ¥ most calculators will give -E- or ERROR
The two special right triangles were used for exact values for 45°, 30° and 60°
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Quite a bit of material has been presented in this lesson. These exact values for the six trigonometric
functions for special angles have wide application, so it is a good idea to memorize some
(45° for example ) and memorize the three diagrams needed to find other values.
Activity 1. Redraw the three diagrams in your notebook
Activity 2: Draw this chart in your notebook and complete some of it from memory and
the rest from the diagrams or your calculator for the quadrantal angles.
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