Trigonometry conventions are used to examine the
geometric properties of a right
triangle. The trigonometric functions are based
on these conventions along with the Pythagorean Theorem.
The theorem states that if a right triangle has two sides a
and b and a hypotenuse
c, then a squared
plus b squared will equal
c squared. This equation can be used to examine
the angles and the sides of any right triangle. As a convention, to examine
trigonometric functions the unit circle
with a radius of one is placed on the origin
at the center of the Cartesian Plane. In this circle
a right triangle is placed with the angle being examined at the origin and
using the radius of the circle as the hypotenuse. The other two sides are
identified as the adjacent side a, and the opposite
side b, as compared to the angle being analyzed.
The opposite side is not touching the
angle but on the opposite end of the triangle and the adjacent
side is touching the angle at the origin. In this way the adjacent
side a is equal to the x
variable and the opposite side b
is equal the y variable, and the hypotenuse c
is always equal to one. The Pythagorean theorem becomes x
squared plus y squared equals one. The angle
at the origin point can be called theta. It is
situated between the adjacent side and the hypotenuse. The six main trigonometric
sine, cosine, tangent,
cotangent, secant and cosecant
examine the properties of the angle theta.