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.