Posted in big in finland, ninja maths, trigonometry.

“$\cos^{-1}(0.93333)$, said the student. A GCSE student, struggling a little; the Mathematical Ninja bit his tongue rather than correct him to $\arccos$ or to $\frac {14}{15}$; he also accepted, grudgingly, the answer was going to be in degrees. “Maybe 21 bad degrees?” “21.04”, said the student. “Not too terrible.” “I

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Posted in ninja maths, trigonometry.

"Have you seen this trick?" asked the student. "If you know all three sides of a right-angled triangle, you can estimate the other angles - $A \simeq \frac{86a}{\frac b2 + c}$!" The Mathematical Ninja thought for a moment, and casually threw a set-square into the wall, millimetres from the student's

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Posted in circles, geometry, trigonometry.

Here's a nice use of circle theorems: ever wondered why the sine rule works?

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Posted in gcse, triangles, trigonometry.

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

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Posted in gcse, triangles, trigonometry.

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

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Posted in gcse, triangles, trigonometry.

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

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Posted in ninja maths, trigonometry.

"So, $\sin(x) = 0.53$," said the student. "32 degrees," said the Mathematical Ninja. The student frowned - the Mathematical Ninja's showing off was starting to wear her down - and typed it into the calculator to check. "$32.005^º$, actually." "I'll take that," said the Mathematical Ninja. "How did you guess

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Posted in ninja maths, trigonometry.

The Mathematical Ninja surreptitiously pressed a button under the table. There was a flash, a sizzle and a slight smell of burning. The student prodded the on-button of his calculator increasingly frantically. "Oh dear," said the Mathematical Ninja. "It must have been a passing electromagnetic storm that's permanently fried the

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Posted in geometry, triangles, trigonometry.

In a recent Maths Challenge, students were told the area of a triangle ($7$cm$^2$) and the length of two of its sides ($6$cm and $8$cm), and asked how many possible lengths there were for the third side. It's easy enough to show there are two: let the base of the

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Posted in circles, core 3, geometry, trigonometry.

Ask virtually any maths teacher what $\sec(\alpha)$ means, the chances are they'll say "it's $\frac{1}{\cos(\alpha)}$," without missing a beat. Ask them what it means geometrically... well, I don't want to speak for the teaching profession as a whole, but I'd have been stumped until the other day. As with the

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