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.
Part of that is the way it’s taught. Students are taught the “unit circle” and its relationship to trigonometry, but many fail to make the leap on how crucial circles are for trig functions.
With static graphs and equations, it’s possible to get a handle on the rules of what various functions do and mean. However, it’s still hard to get an intuitive sense of the relationship between the circle and the trigonometric functions and the triangles.
That all changes with animated GIFs. Change over time is crucial to understanding trig. With pictures like these — found on Imgur from an album linked in Reddit’s peerless Math subreddit— trig becomes a breeze.
For starters, here’s 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: