There are two "special" right triangles with which you need to be
familiar; the 45º- 45º- 90º triangle and
the 30º- 60º- 90º triangle. The "special"
nature of these triangles is their ability to yield exact answers
instead of decimal approximations when dealing with trigonometric
These triangles will be used
continually throughout your studies of mathematics and are well worth
your time and study.
The most powerful method of
working with these triangles is to work directly with the
triangles themselves. By remembering the "relationships" in
these triangles, you will have the power to apply any of the six
trigonometric functions in any situation.
Some people find charts helpful for
remembering the trigonometric values of 30º, 45º, and 60º.
Unfortunately, memorizing charts of information often gives you a
limited understanding of the concepts at hand. For example, if a chart is limited to only a few of the trigonometric functions,
such as the charts seen below, your "power" to solve a
multitude of problems is also limited.
This chart shows the values
This chart shows a "trick"
for remembering the values. Notice the row for sin
shows 1, 2,
3 under the radicals, while the
row for cos shows 3, 2, 1
under the radicals.
Let's move on to studying the triangles themselves.