Trigonometry-TK Maths

TK Maths, Ronan Downes, Mar 18, 2020

SOHCAHTOA to Basic Trig Identities

Table of Contents

  1. Basics
    1. 3 - Geo - Right Angled Trig
    2. 3 - Geo - Trig Graphs
  2. 3D
    1. 4,5 - Geo - 3D Pythagoras'
    2. 4,5 - Geo - 3D Trig Cuboid
    3. 4,5 - Geo - 3D Trig Pyramid
  3. Special Angles
    1. 4,5 - Geo - sin, cos, tan of 45deg
    2. 4,5 - Geo - sin, cos, tan of 30 and 60deg
  4. Beyond 0-90 Degrees
    1. 5 - Geo - Unit Circle for angles bigger than 90
    2. 4,5 - Geo - Trig Graphs beyond 0-90deg
  5. Sine & Cosine Rules
    1. 4,5 - Geo - Sine Rule Proof
  6. Transforming Trigonometric Graphs
    1. 6,7 - Geo - sin(x) Transformations
    2. 6,7 - Geo - cos(x) Transformations
    3. 6,7 - Geo - tan(x) Transformations
  7. Cosecant, Secant and Cotangent
    1. 6,7 - Geo - cosec, sec & cot Graphs

1.

Basics

The basics of trigonometry [list] [*]Trig Graphs [/list]

  • 1. 3 - Geo - Right Angled Trig
  • 2. 3 - Geo - Trig Graphs

1.1.

3 - Geo - Right Angled Trig

Move the vertices of the triangle.[br]Click the boxes to show/hide sin, cos and tan.
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1.2.

–

2.

3D

  • 1. 4,5 - Geo - 3D Pythagoras'
  • 2. 4,5 - Geo - 3D Trig Cuboid
  • 3. 4,5 - Geo - 3D Trig Pyramid

2.1.

4,5 - Geo - 3D Pythagoras'
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2.2.

–

2.3.

–

3.

Special Angles

30, 60 an 45 Degrees

  • 1. 4,5 - Geo - sin, cos, tan of 45deg
  • 2. 4,5 - Geo - sin, cos, tan of 30 and 60deg

3.1.

4,5 - Geo - sin, cos, tan of 45deg

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3.2.

–

4.

Beyond 0-90 Degrees

Unit Circle Symmetry in the graphs

  • 1. 5 - Geo - Unit Circle for angles bigger than 90
  • 2. 4,5 - Geo - Trig Graphs beyond 0-90deg

4.1.

5 - Geo - Unit Circle for angles bigger than 90

Choose which quadrant you wish to see based on the angle you are considering[br][list][br][*]2nd Quadrant: 90-180 Deg[br][*]3rd Quadrant: 180-270 Deg[br][*]4th Quadrant: 270-360 Deg[br][/list]
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4.2.

–

5.

Sine & Cosine Rules

  • 1. 4,5 - Geo - Sine Rule Proof

5.1.

4,5 - Geo - Sine Rule Proof

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6.

Transforming Trigonometric Graphs

Given f(x) = sin(x) tan(x) or cos(x), what are the results of changing a, b, c and d in y=a f(bx+c)+d

  • 1. 6,7 - Geo - sin(x) Transformations
  • 2. 6,7 - Geo - cos(x) Transformations
  • 3. 6,7 - Geo - tan(x) Transformations

6.1.

6,7 - Geo - sin(x) Transformations

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6.2.

–

6.3.

–

7.

Cosecant, Secant and Cotangent

  • 1. 6,7 - Geo - cosec, sec & cot Graphs

7.1.

6,7 - Geo - cosec, sec & cot Graphs
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