TRIG Functions

What are TRIG functions?

In this blog post, I would like to talk about Trigonometry functions (or Trig functions for short). These functions are a source of confusion for many students, so I will try to address the confusions.

The main 3 trig functions are Sine, Cosine, and Tangent. These are functions that take an angle as input, either in degrees or radians and give a unit-less number as the output. Usually they will be written as sin(θ), cos(θ), or tan(θ), and read like sine theta, cos theta, and tan theta. Every function needs an input. Here, that input is just given the name theta with symbol θ.

If you draw a right-angle triangle (triangle with a 90-degree angle), you can define these 3 functions as ratios of the sides of the triangle. First, let’s choose the lower right angle as angle θ. The biggest side of the triangle, the one that’s in front of the 90-degree angle, is called the hypotenuse (hyp). In the triangle below, that is length c. The side that is opposite (in front) of the angle is called the opposite (opp). In the triangle below, that is length a. The side that is connected to angle θ but not the hypotenuse, is called the adjacent side (adj). In the triangle below, that is side b.

Once we have have established the sides, we can define the trig functions. sin(θ) is defined as the length of opposite (a) divided by length of hypotenuse (c). cos(θ) is defined as the length of adjacent (b) divided by the length of hypotenuse (c). tan(θ) is defined as the length of opposite (a) divided by length of adjacent (b).

These functions help us determine the ratios of lengths of sides of triangles relative to the angles of the triangle.

If you have read this post and have questions on this topic or other math and physics questions, feel free to get in contact with me via this website. Thank you for taking the time to read my content!