Trigonometry

Here is what you should really think when you see the number π:

Many people are confused about what radians are. Well, there’s a GIF for that:

Next, think about the relationship between sine, cosine and the circle.

Here’s an illustration of the fundamental relationship between the three.

Notice how the crank moves in a circle, and the bars – which correspond to sine and cosine – move up and down and side to side in a wave-like formation.

Here’s a more traditional demonstration of sine and cosine. You make your way around the circle (black). As you do, the values of Y translate to sine (red line) and the values of X translate to cosine ( blue line).

Now, let’s start linking this relationship between the functions and circles to triangles:

The triangle relationship is crucial to the definition of the tangent () function. The intersection of the triangle’s hypotenuse line with the vertical line along the right side of the circle defines the function.

Here’s another way of looking at it, without the triangle: