## Ask Uncle Colin: Trouble in Sector ABC

Dear Uncle Colin, I got stuck on this sector question, which asks for the radius of circle $P$, which touches sector $ABC$ as shown. I'm given that $ABC$ is a sector of a circle with centre $A$ with radius 12cm, and that angle $BAC$ is $\frac{\pi}{3}$. My answer was 3.8cm,

## Radians (and why they are better than degrees)

The brilliant @dragon_dodo has written a cartoon to explain - as if explanation were needed - of why radians are the correct way to measure angles.

## Angle patterns on the unit circle

The student blinked, and the Mathematical Ninja had covered the board in a colourful diagram. "It's easy," said the Mathematical Ninja, "to work out the fractions of pi in each quadrant - once you know a few rules." The student automatically reached for a pen. Whenever the Mathematical Ninja mentioned

## Secrets of the Mathematical Ninja: Sine, cosine and what they really mean (part I)

"Oh," says the student, "I'll just put it in my calculator." I fold my arms. "$\sin\left(\frac{\pi}{6}\right) = 0.00914$!" he says, confidently. I sigh. "Oh!" he continues, brightly, "is it meant to be in radians? I don't like radians." This is the problem with calculators Now, I love calculators. Machines that

## Secrets of the Mathematical Ninja: Sines and cosines near 45º

This is the one area where I'm better with degrees than with radians - and I suspect that's only because I don't particularly notice when radian angles are close to $\frac{\pi}{4}$, but I do when degree angles are close to 45º. This one's a trickier one than we've been looking

## The Secrets of the Mathematical Ninja: The World's Third Most Famous Triangle

My favourite trick, when I was helping students at the Physics Homework Centre at Montana State University, was to eyeball a question for a moment and say "... which is, what, 53.13 degrees or so..." without batting an eyelid. The poor students! There they were trying to figure out which

## Secrets of the Mathematical Ninja: Converting degrees into radians

I'll hold up my hands here and say: most of the secrets of the mathematical ninja are guides to showing off. Few of them have much practical use beyond making everyone else in the class look at you funny. This one - converting degrees into radians - is different. If

## Why radians rock (and degrees don’t)

If I could wave a magic wand and overhaul just one thing to make the world a better place, I'd have a tough choice. Would I get rid of the QWERTY keyboard in favour of a more sensible layout? Would I make the English language fonetik? Would I take maths