# Special Angles

• May 27th 2009, 12:05 PM
VonNemo19
Special Angles
Anybody out there have a good acronym, or system for remembering the values of the trig functions at the special angles(e.g. $\displaystyle 0,\frac{\pi}{6},\frac{\pi}{4},\frac{\pi}{3},\frac{ \pi}{2}.....)$ ? I'v got a test coming up that's being timed, so I can't be reproving them while taking the test.
• May 27th 2009, 01:54 PM
pickslides
I get by on memorising 2 triangles and the general shapes of the functions.
• May 27th 2009, 07:00 PM
VonNemo19
Could you elaborate. Are talking about equilateral and isosoles triangles, where the equilateral has each side equal to 2? And the isosoles with legs=1, and hypotenuse=$\displaystyle \sqrt{2}$?

But, that's kind of like having to reprove the thing to myself again, whereas I would kind of like something that's much faster. Everyone knows PEMDAS. It's easy and fast.

Here's one for the trig functions themselves:

SOH-CAH-TOA (soak-a-toe-a)

$\displaystyle \sin=\frac{o}{h}$ sin is opposite over hypotenuse

$\displaystyle \cos=\frac{o}{h}$ cos is adjacent over hypotenuse

$\displaystyle \tan=\frac{o}{a}$ tan is opposite over adjacent

This is what I'm after.
• May 28th 2009, 02:00 PM
pickslides
Quote:

Originally Posted by VonNemo19
Could you elaborate. Are talking about equilateral and isosoles triangles, where the equilateral has each side equal to 2? And the isosoles with legs=1, and hypotenuse=$\displaystyle \sqrt{2}$?

I am talking about those triangles. I have no way of remembering the values. If anything I have just remembered (burnt images of them into the back of my mind) what they look like. The least amount to put to memory is to consider the isosoles triangle has equal similar lengths of 1. From there if need be you should be able to work out the long side using pythagoras and in turn the angles present themselves. Same with the equilateral of length 2, obivously this triangle has equal angles of $\displaystyle \frac{\pi}{3}$ . Once you drop a perpendicular line down the middle of it all the other values and angles present themselves.

I also put to memory the function shapes over one cycle of sine, cos and tan. This helps you solve for $\displaystyle 0,\frac{\pi}{2}, \pi, \frac{3\pi}{2},2\pi$.

Quote:

Originally Posted by VonNemo19
Here's one for the trig functions themselves:

SOH-CAH-TOA (soak-a-toe-a)

Can't go wrong with that one. It's a timeless classic. If mathematicians put out a "greatest hits" of mathematical acrynoms. This would be the lead off track! (Rock)