Right triangle definitions of trig functions and related applications

From Department of Mathematics at UTSA
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Some of the most fundamental trigonometric identities are those derived from the Pythagorean Theorem. These are defined using a right triangle:

right triangle

At this stage in the course the Pythagorean Theorem should be second nature to you. If you have not yet learned it, learn it now.

and of course are the legs or the adjacent and opposite edges, and is the hypotenuse, the longest side, the side that does not include the right angle. This formula only works for a right angle triangle. If the angle shown as a right angle in the diagram were obtuse, larger than a right angle, then would be larger than the Pythagorean sum. If the angle shown as a right angle were smaller than a right angle, then would be smaller than .


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