# 7 GIFs That Will Make You Instantly Understand Trigonometry

Trigonometry is the branch of math that studies triangles, with a particular focus on the relationships between angles and the lengths of corresponding sides.

Interestingly enough, the trigonometric functions that define those relationships are also closely tied to circles.

Needless to say, this makes trig one of the hardest topics in math for students to grasp intuitively.

## 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 so, the values of Y translates to sine (red line) and the values of X translate to cosine (blue line):

## 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:

Is this the way math should be taught?

`Source: Walter Hickey, Bussines Insider`

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