What are Trigonometric Functions?
The trigonometric functions are a set of equations that are used to represent the ratios between the side lengths of a right-angled triangle. There are six main trigonometric functions: Sine, Cosine, and Tangent, and their reciprocals Cosecant, Secant and Cotangent.
Example:
Calculate the six trigonometric functions for an angle x of a right-angled triangle if the length of the opposite side is 5 and the hypotenuse is 13.
First, as the triangle in question is right-angled, the measure of the adjacent angle can be easily found by using Pythagoras’ theorem.
We can now use the values we have to calculate all six of the trigonometric functions:
In what other ways can we interpret Trigonometric Functions?
The trigonometric functions can also be represented in terms of the unit circle that is on a coordinate plane. A unit circle is a circle which has a radius of one unit.
Since the hypotenuse of the right- angled triangle is also the radius of the unit circle, it has a unit of 1. This means that both sin(z) and cos(z) will be equal in magnitude to the length of the opposite and adjacent sides respectively. Therefore, sin(z) and cos(z) are equal to the vertical (y) and horizontal (x) distances from the origin.
What are Trigonometric Identities?
Would it be possible to relate the six trigonometric functions to one another so that our calculations are simplified?
What is Pythagoras` Theorem?
Pythagoras’ Theorem states that the square of the hypotenuse is equal to the sum of the squares of the opposite and the adjacent sides.
