Monday, May 9, 2011

How Right Triangle become important part of Trigonometry

Trigonometry, means the measure on a trigonal. Formally we say that trigonometry is branch in mathematics that studies triangle and the relation between the angles and the sides. When you learn it at school, you know that right triangle become an important part. Why? and where it come from?

Let we talk bout the property of congruent triangle. They say that if two triangle is congruent, which mean the associate angle is equal, proportion of its associate sides is equal to each other.

Lets use it in trigonometry. Trigonometry relate an angle of a triangle to the proportion of it sides. Since we use an angle, not angles, we do not have any suggestion where triangle in question. Say 30 degree of an angle, so we can build up unlimited triangle of it.

Thats the key to trigonometry of right triangle. On a right triangle, if we define a degree (of course which absolute of it should less then 90 and not equal to zero), we can build an unlimited triangle, but with special property that they are congruent. Since the congruency tell us that its not affect on the angles and the proportion of sides (note its not their weight or length), so on a right triangle, an angle is relate to proportion of two sides. if the sides describe depend on the unique angle, we can listed trigonometric proportion of right triangle below.

sin a = opposite/hypotenuse
cos a = adjacent/hypotenuse
tan a = opposite/adjacent

hypotenuse is familiar term on right triangle specially when you talking pythagorean. Opposite and adjacent is side that depend on the unique angle 'a'. And the sin, cos, tan, is refer to sines, cosines, and tangent as a trigonometric function.

That is a unique of an angle on right triangle, that combine with the congruency of triangle, build up a trigonometric proportion. in extend of that proportion, there are several function that related to the mention above is secant, cosecant, and cotangent. This is how math build on your mind.

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