Browsing category trigonometry

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

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Remembering how to differentiate – Secrets of the Mathematical Ninja

The Mathematical Ninja makes ample use of mnemonics to remember how to do just about everything. He was quite upset when Pluto was demoted, because "My Very Easy Mnemonic Just Serves Up Nine" doesn't make any sense. In particular, the Mathematical Ninja has a creed. A strict set of rules

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R sin alpha: Secrets of the Mathematical Ninja

Dealing with the R sin alpha nonsense that comes up in C3 is the kind of thing our arch-nemesis, the mathematical pirate, would grumble about constantly. They’d claim it wasn’t really trigonometry, or just that it was too hard, or a complete misuse of the word ‘arr’. The mathematical ninja,

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How to do a trigonometry proof: five top tips

First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they're closer to 'real' maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry1. And a lot of students struggle with it

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How to do a trigonometry proof: five top tips

First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they're closer to 'real' maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry1. And a lot of students struggle with it

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How to do a trigonometry proof: five top tips

First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they're closer to 'real' maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry1. And a lot of students struggle with trigonometry

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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

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Secrets of the Mathematical Ninja: Trigonometry With Small Numbers

Radians - as I've ranted before - are the most natural way to express angles and do trigonometry. No ifs, no buts, degrees are an inherently inferior measure and the sooner they're abolished, the better. (In other news, the campaign to replace the mishmash of units called 'time' by UNIX

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The trig identities you need to know for integration

There is one big-daddy among the trig identities that you need to learn right now, if you don't know it already: $$\sin^2(x) + \cos^2(x) = 1$$ This is the identity that nearly all of the others spring from. There are some more definitions: $tan(x) = \frac{\sin(x)}{\cos(x)}$, which is one of

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