# Quod Erat Demonstrandum

## 2017/06/10

### 正多邊形方程

Filed under: Additional / Applied Mathematics,Fun,mathematics,NSS — johnmayhk @ 12:24 下午
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https://www.desmos.com/calculator/vv7stc4nl0

## 2016/12/11

### 小心出題

Filed under: mathematics,NSS — johnmayhk @ 11:18 下午
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$AB=\sqrt{30^2+45^2-2(30)(45)\cos(60^o-40^o)}=19.7$ m

$AB=45\cos 40^o-30\cos 60^o=19.5$ m

## 2016/06/14

### 正七邊形

Filed under: Fun — johnmayhk @ 12:07 上午
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（習題）從片中某些結果不難推出以下命題： (more…)

## 2016/03/21

### 用Ｄ證trigo

Filed under: Additional / Applied Mathematics,NSS — johnmayhk @ 11:13 上午
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Prove the following identity

$\cos^2x+\cos^2(x+y)-2\cos y\cos x\cos(x+y)=\sin^2y$.

## 2015/10/11

### 正四面體，兩個夾角

Filed under: Fun — johnmayhk @ 9:10 下午
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1.一個玩具

## 2015/10/07

### 三角題

Filed under: NSS — johnmayhk @ 2:58 下午
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Just come across a part of a core mathematics trigonometry problem today morning, I and my student used different ways to solve it, but actually, same results turn up:

Given

$AC=b$,

$CB=a$, where $a > b$

$\angle CAB=\theta < 90^o$,

find $c$ in terms of $a,b,\theta$.

(Note: this is an ‘A.S.S.’ given, but the triangle can be uniquely determined.)

Method 1 (more…)

## 2015/08/03

### 小學三角題

Filed under: Junior Form Mathematics — johnmayhk @ 4:34 下午
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Whatsapp 傳來同事阿仔的暑期功課：在釘板上圍出一個等邊三角形

## 2015/05/20

### 幾何老題

Filed under: Fun — johnmayhk @ 1:40 下午
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$x$ 的大小。（圖有誤，$\angle ACD=30^o$，非 $60^o$

## 2015/05/19

### 某中三三角學題

Filed under: Junior Form Mathematics — johnmayhk @ 11:47 上午
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Given that $\tan \theta=\sqrt{2}$, where $\theta$ is an acute angle. Using trigonometric identities, find the value of $\sin^2\theta - \cos^2\theta$.

## 2014/12/19

### 某些M2題

Filed under: NSS — johnmayhk @ 9:30 下午
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Q.1

$\sin\theta+\cos\theta=\frac{7}{3}$　時，同學已指出：冇可能！因為 $\sin\theta$$\cos\theta$ 的最大值不過是 1。

Q.2

## 2014/01/07

### Core Math 小題

Filed under: NSS — johnmayhk @ 2:34 下午
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$a^2+b^2=c^2$，即該三角形是直角三角形。

A. $a^2+b^2 > c^2$ 還是
B. $a^2+b^2 < c^2$

（停一停，想一想）

(more…)

## 2012/11/19

### [FW] 國小三角數學題爭議！

Filed under: Fun,Junior Form Mathematics — johnmayhk @ 12:47 下午
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## 2010/11/25

### 弧度

Filed under: NSS — johnmayhk @ 12:40 下午
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$s = r\theta$$\theta$ is measured in radian）

$180^o = \pi$ radian

$\pi r = r \theta$

(more…)

## 2010/05/13

### Trivial sharing on trigonometry

Filed under: Additional / Applied Mathematics,mathematics,NSS — johnmayhk @ 7:33 上午
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What’s wrong with the following steps?

$\sin\theta < 0$

$\Rightarrow \theta$ lies in the 3rd or 4th quadrant (more…)