How To Easily Remember the Unit Circle

I work in a walk-in tutor lab at my university and one of the other tutors showed me this a couple years back and it has changed my life.

First, you make a table that looks like this.

Then, go ahead and add in some nice denominators of 2 in every entry in the table.

Then give yourself some nice square roots on the numerators.

Alright – now we’re going to fill it in. The only value you have to remember is that sin(0)=0. So we put 0 in the numerator for 0 in the sine column. Then we just count up as we move down.

Then we do the opposite in the cosine column.

Then we simplify!

And voila – a beautiful unit circle table.
A 3,700 year old Babylonian tablet rewrites the history of maths
“The Babylonians unique approach to arithmetic and geometry means this is not only the world’s oldest trigonometric table, it’s also the only completely accurate trigonometric table on record,” he said.

The Ancient Babylonians knew about a form of trigonometry more advanced than the modern-day version – about 1,000 years before its supposed invention by the Ancient Greeks, academics in Australia say.

The astonishing claim is based on a 3,700-year-old clay tablet inscribed with a table of numbers.

Known as Plimpton 322, it is already known to contain evidence that the Babylonians knew Pythagoras’ famous equation for right-angled triangles, long before the Greek philosopher gave his name to it.

And researchers at the University of New South Wales (UNSW) have claimed it also shows the Babylonians developed a highly sophisticated form of trigonometry – the system of maths used to describe angles that has tortured generations of school pupils with sine, cosine and tangent.

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I really love this crayola supertips color 💕 I just had a trig quiz today, so here are some math notes :3
「Quick tip: When reviewing for a math quiz, practice problems are a great way to refresh the procedures in your mind~」

This is my trick for remembering trigonometric values. Forget memorizing those little charts or triangles, this is so much easier. 

I learnt this in 10th grade from my favorite teacher (who wasn’t actually my maths teacher at the time) and I still used it for the rest of High School and will probably continue to use it in University.

So what do you do? You draw the chart in the picture. That one. 

OK, but how do you read it? Like a table. (If you’re unfamiliar with radians, do not worry. It also works in degrees, just write: 0, 30, 45, 60, 90 instead.)

For example, if you want to find the sin(pi/2), you simply start at sin(x) and then move over until you’re at pi/2 (or 90 degrees). It says sqrt(4). Now you put that over 2, and you have it. Sin(pi/2) = (sqrt(4))/2, also known as 2/2, or 1. 

If you want to find the cos(pi/4), you do the same thing: start at cos(x), move until (pi/4). It says sqrt(2), now put that over 2, and you have cos(pi/4) = sqrt(2)/2.

For tan(x), just take the sin(x) value and divide it by the cos(x) value!

So tan(pi/6) = sqrt(1) / sqrt(3) = 1/sqrt(3).

I find this so easy to remember because the first line starts at zero and increases, and the second line starts at 4 and decreases. It works for any values (yes, even ones above pi/2!) and it’s so simple. I encourage you to start by writing it out on every paper, when you’re studying, and on your exams. 


Feb. 6, 2018 - 20/100 days of productivity

So I was allowed to skip school today to study for my trig and physics tests at the end of the week and to start my IRR so I went straight to Starbucks. The Pomodoro Technique thing is a godsend. All I have to say right now is…. physics…honey….wyd….

Listening to: Runaway by Against The Current

How I memorise formulas

We’ve all been in that position where we’re completely thorough with the solving of a math / physics problem and the only place where we go wrong is the formula (well, at least I am :/). How am I supposed to make sure that I do not mess up my formulas?

You can try what I did for an oral test on trigonometric identities, because that one went really well even though it wasn’t a write enough test and we were supposed to answer rapidly?

Here’s what I did :

When the test was announced : nothing really, I just put up a sticky note on my desk reminding me about the test

3 days before the test : I wrote down all the formulas on a sheet of paper, and went through them once.

2 days before the test : I recalled the formulas (without looking at them) twice throughout the day, once while having my breakfast and next when brushing my teeth and preparing for bed.

1 DAY BEFORE THE TEST luckily for me this was a Sunday so I had plenty of time to revise.
I went through them once while having breakfast (lol that’s my fav time for studying idk why), next when I had absolutely nothing to do aka the 2pm ~ 3pm time slot.
I kind of mugged them up once just to make sure I don’t forget them (it’s not recommended tho cuz this may not work for everyone).
I noted the formulas down on another sheet without peeking at all.
Finally I babbled them out to my mom who happens to be my Guinea pig for study related stuff (literally, like if you guys want I can list out a 100 ways in which she helps me study).
Boom, that’s it! I was confident by then and it helped me speak clearly (and not choke on my spit) in the class!

Try these tips out and if they do work, let me know ;)



19th February 2017 • day 4/100 • a few late trig notes to keep my mind awake as I’m feeling ill today. I love how cute these notes are and the colours are perfect!! I got the idea for the style of notes off a post I saw earlier, but I’m not sure who it was now, but it’s VERY cute :)
Tomorrow I’ll be back to full-on studying, so I’ll have more studyspo for next week.