Trigonometry Functions: Three Functions, Same Idea.

Right-Angled Triangle:

"Opposite" is opposite to the angle θ
"Adjacent" is adjacent (next to) to the angle θ
"Hypotenuse" is the longest side

Before we start with the three trigonometric functions - sine, cosine and tangent, we will first look at a summary of them below:

These circular functions are functions of an angle, used to relate the angles of a triangle to the lengths of the sides of a triangle. The functions are important in the study of triangles and modeling periodic phenomena, among other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. Below is a description for each function:

Sine: taking an angle and finding the length of the y-component (rise) of that particular right-angled triangle.

Cosine: taking an angle and finding the length of x-component (run) of that particular right-angled triangle.

Tangent: taking an angle and finding the slope (y-component divided by the x-component) of that particular right-angled triangle.

Trigonometric functions are usually represented in ratios of two sides of a particular right-angled triangle, like the following:

Using the functions is relatively simple - you only need to know either the two other sides or one side with the theta.

Thus, for a right-angle triangle with an angle θ , the functions can be calculated:

Sine Function: sin(θ) = Opposite / Hypotenuse
Cosine Function: cos(θ) = Adjacent / Hypotenuse
Tangent Function: tan(θ) = Opposite / Adjacent

Here are 2 examples:

Example 1: what are the sine, cosine and tangent of 30° ?

The classic 30° triangle has a hypotenuse of length 2, an opposite side of length 1 and an adjacent side of √(3):
Now we know the lengths, we can calculate the functions:Sine sin(30°) = 1 / 2 = 0.5
Cosine cos(30°) = 1.732 / 2 = 0.866
Tangent tan(30°) = 1 / 1.732 = 0.577