230-Trigonometry

Arthur Lee, Ronan Downes, 11 Mar 2020

Trigonometric Ratios and Functions

Table of Contents

  1. Right Triangles
    1. Introduction to Sine
    2. Trigonometric Ratios: Sine 三角比：正弦
    3. Introduction to Cosine & Tangent
    4. Trigonometric Ratios: Cosine & Tangent 三角比：餘弦和正切
    5. Simple Sine Table
    6. Sine and Cosine Table
    7. recognise trigonometric ratios
    8. Quiz on Trigonometric Ratios 辨認三角比：測驗
    9. trigonometric ratios for all angles
    10. 任意角的三角比
    11. Regiomontanus
  2. trigonometric functions
    1. Trigonometry and Polar Coordinates
    2. Random point with trigonometric details
    3. Polar and Rectangular
    4. Introduction to Polar Coordinates 極坐標簡介
    5. 極坐標測驗
    6. polar and spiral
    7. Proof without words: Cosine Rule (餘弦公式)
  3. making patterns and animation
    1. Sinimation
    2. sine curve rotated
    3. Cosine Shift
    4. Dot Pattern 1
    5. Dot Pattern 2
    6. Dot Pattern 3
    7. Happy Halloween
    8. Halloween with sound
    9. sun and sea
    10. Moon and Sea

1.

Right Triangles

introduce trigonometric ratios in Key Stage 3 (junior secondary level), focusing on sides and ratios in right triangles

  • 1. Introduction to Sine
  • 2. Trigonometric Ratios: Sine 三角比：正弦
  • 3. Introduction to Cosine & Tangent
  • 4. Trigonometric Ratios: Cosine & Tangent 三角比：餘弦和正切
  • 5. Simple Sine Table
  • 6. Sine and Cosine Table
  • 7. recognise trigonometric ratios
  • 8. Quiz on Trigonometric Ratios 辨認三角比：測驗
  • 9. trigonometric ratios for all angles
  • 10. 任意角的三角比
  • 11. Regiomontanus

1.1.

Introduction to Sine

– GeoGebra Institute of Hong Kong, Alex CHIK

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

trigonometric functions

define trigonometric functions for angle of rotation

  • 1. Trigonometry and Polar Coordinates
  • 2. Random point with trigonometric details
  • 3. Polar and Rectangular
  • 4. Introduction to Polar Coordinates 極坐標簡介
  • 5. 極坐標測驗
  • 6. polar and spiral
  • 7. Proof without words: Cosine Rule (餘弦公式)

2.1.

Trigonometry and Polar Coordinates

This applet focuses on the conversion between rectangular and polar coordinates. [br]Even without formal knowledge about polar coordinates, we can still ask how the direction and distance of a point from origin could be related to the usual coordinates, with a useful definition of sine and cosine values. [br][br]When you hide some of the values on the left, you can practise your estimation.
– Arthur Lee

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2.7.

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3.

making patterns and animation

create patterns, animation, drawing using trigonometric and other functions/graphs

  • 1. Sinimation
  • 2. sine curve rotated
  • 3. Cosine Shift
  • 4. Dot Pattern 1
  • 5. Dot Pattern 2
  • 6. Dot Pattern 3
  • 7. Happy Halloween
  • 8. Halloween with sound
  • 9. sun and sea
  • 10. Moon and Sea

3.1.

Sinimation

Sinimation! Have fun with a simple sine curve animated.
Sinimation
Can you recognise the sine graph and parameters making this pattern? [br]Pause the animation. Drag a and b to experiment or look for an image you like.
– Arthur Lee

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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Information