Saturday, January 10, 2009

Trigonometry: Degrees and Radians

I have decided to take up reviewing trigonometry as a goal for this blog. In the first look at trigonometry it is necessary to understand angles. Angles are create by the intersection of two lines. They can be measured in degrees or radians.

There are 360 degrees in any possible angle, the widest angle forming a complete circle. The number 360 was chosen by the Babylonians who counted in groups of 60 (base 60) where as we count in groups of 10 (base 10). Thus 1/60th of a degree is called a minute and 1/60th of a minute is called a second. This terminology is still used by navigators today, but some also use decimals. In any case, two perpendicular lines, like in a capital L are said to have 90 degrees, a flat line ___ has 180 degrees and flipping the whole thing over completes the circle with 270 degrees and finally 360.

Radians are ways of measuring angles as they are drawing inside a circle. If we take the circumference of a circle we get C = 2(pi), thus we can draw a unit circle (circle with circumference = 1) around any angle and be able to express the measure of that angle in terms of radians. Thus the L would become (Pi/2) or 1/4 the circumference, which also equates to 90 degrees. The flat line ___ would become Pi, or half the circle, this would equate to 180 degrees.

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