How Sine, Cosine, and Tangent Work In Mathematics



So Sine, Cosine, and Tangent are all used a lot in Hopscotch a lot, but I am going to teach you how they work in mathematics, and maybe that will help you understand in Hopscotch.

Warning: If you have not taken Algebra I, some of this might be confusing to you, fair warning!

Ok, so first things first, what is Sine, Cosine, and Tangent? The answer is that they are all forms of equations used to help find proportional triangles, or in simpler terms, it just helps you find what triangles are similiar. However, the equations only work with Right Triangles, and are mainly used in 30/60 Right Triangles, which are Right Traingles that have angles measuring 90, 60, and 30 degrees.
Refer to this image:

Sine is a proportion you get when you divide the Opposite side by the Hypotenuse. If we were to call the top angle of this triangle (the 30 degree angle) A, sinA would be looking at the opposite side of angle a, which in this case is leg X, which would be divided by the hypotenuse, which is 2x. So the proportion for this triangle would be 1/2.

Cosine is similiar form of Sine, in which you divide the Adjacent leg by the Hypotenuse. In the case of this triangle that would be x times √3 divided by 2x, which is roughly 8.66.

Tangent is weirder, because the Hypotenuse is not included in the equation. It goes opposite side divided by the adjacent side. tanA for this triangle would be x divided by x√3, which would just be √3.

There is also Reverse Tangent, which is just Adjacent divided by the Opposite side.

Hope this tutorial helped!


@sarcastictvhead here is a genuine LEGO life Garmadon head emoji.

As far as I know only us two and the LEGO guys have one


Excuse me don’t


Or…Trigonometric ratios

Aka: Longest side of right triangle

I always wondered about that.


Well to bad for me …


There’s something called reversed tangent? Is there reversed sine and cosine too?


Reverse tangent is called cotangent, reversed sine is cosecant and reversed cosine is cosecant.

Great topic! You have your definitions of ratios right, but I think you may need to double check a few of your examples :slight_smile: (what’s x/2x?)


Wow! Great topic!!! I think this is very helpful


I believe in Hopscotch it was referred to as Reversed ___ so that’s why I used it here


That’s true, but the mathematical definition is the side opposite to the right angle


Great tutorial! I’d try to get it to make sense in my mind (I’ve never done Algebra) if I didn’t want to think about math for as long as possible!

Why don’t you tag pomtl?


There are so many people asking about this, so thank you for making this amazing tutorial! I will share this when somebody asks about sin, cos, tangent or all of them.

I am starting to get a little bit worried though: could we talk about math in the USA on my general topic? Because, in Sweden, our books still have assignments like 6,7 + 1,8 in 9th grade.


Nice topic! This is a great tutorial because I always see people asking about sin or cos or tangent.


Because this topic is not related to the making of a specific project.

Hey scotch, I appreciate the amount of detail you put into a subject some people find a little “overwhelming”.


You’re thinking of the inverse functions.

Different thing.


I know. But the whole purpose of this topic is to get people to understand trigonometric ratios.


not really explained but thanks.