Trigonometry 1 11 th November 2019 Welcome! Trigonometry 1 - - PowerPoint PPT Presentation

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Trigonometry 1 11 th November 2019 Welcome! Trigonometry 1 - - PowerPoint PPT Presentation

Feb 20, 2023 337 likes •541 views

Trigonometry 1 11 th November 2019 Welcome! Trigonometry 1 Question Focused Approach 2 hours - 10mins break at 7pm Feedback form after the break Any questions? Just Ask!! Useful Resource for Project Maths

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SLIDE 1

Trigonometry 1

11th November 2019

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SLIDE 2
  • Trigonometry 1
  • Question Focused Approach
  • 2 hours - 10mins break at 7pm
  • Feedback form after the break
  • Any questions? – Just Ask!!

Welcome!

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SLIDE 3
  • www.themathstutor.ie
  • Normally €99.99
  • Discount code: SAI
  • €49.50 for the year
  • Access to June 2020

Useful Resource for Project Maths

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SLIDE 4
  • Slides, questions and solutions available on our website from tomorrow
  • https://web.actuaries.ie/students/maths-tutorials-higher-level-leaving-

certificate-20192020

  • Or google ‘actuaries.ie maths tutorials’ to find it

Material from tonight

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SLIDE 5
  • Radians & Degrees
  • Length of an Arc
  • Trigonometric ratios
  • Unit circle

What can you expect to get from tonight?

  • Sine Rule
  • Area of a triangle
  • Cosine rule
  • 3D Questions
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SLIDE 6
  • Read the question carefully.
  • Know the vocabulary.
  • Draw a diagram every time.
  • Label all diagrams.

Exam Technique:

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SLIDE 7
  • Check the mode on your calculator – radians or

degrees.

  • Check for the format of your answer; e.g. in terms of π.
  • Include the units.

Exam Technique:

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SLIDE 8
  • Know how to round your answer.
  • Know when to round your answer.
  • Do not round early.

Exam Technique:

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SLIDE 9

Can you explain what a Radian is? Give the definition.

A radian is the measure of the angle at the centre of a circle subtended by an arc equal in length to the radius.

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SLIDE 10

Definition of a Radian

When the arc and the radius are the same size, then the angle in between is one Radian.

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SLIDE 11

Page 13

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SLIDE 12

Each of the trigonometric ratios compare one side of a right angled triangle to one of the other sides. There are six ratios - yes 6. Can you name them and say which side is compared to which? Trigonometric Ratios

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SLIDE 13

Sine, Cosine and Tangent are well known but are given on page 16 of your Formulae book – along with Pythagoras’ Theorem. Cosecant, Secant and Cotangent are the reciprocals of these and are given on page 13. Trigonometric Ratios

Page 16 Page 13

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SLIDE 14

Trigonometric Ratios

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SLIDE 15

Handy way to remember the ratios:

𝐓in 𝑦 = 𝑷𝑞𝑞𝑝𝑡𝑗𝑢𝑓 𝑰𝑧𝑞𝑝𝑢𝑓𝑜𝑣𝑡𝑓 𝐃os 𝑦 = 𝑩𝑒𝑘𝑏𝑑𝑓𝑜𝑢 𝑰𝑧𝑞𝑝𝑢𝑓𝑜𝑣𝑡𝑓 𝑼𝑏𝑜 𝑦 = 𝑷𝑞𝑞𝑝𝑡𝑗𝑢𝑓 𝑩𝑒𝑘𝑏𝑑𝑓𝑜𝑢

SOH CAH TOA

Silly Old Harry Caught A Herring Trawling Off America

Trigonometric Ratios

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SLIDE 16

Beyond the right-angled triangle:

2nd Quadrant 1st Quadrant 3rd Quadrant 4th Quadrant

0° 90° 180° 270° 360° θ° = x° θ° = 180° - x° θ° = 180° + x° θ° = 360° - x° Page 13

Sin + All + Tan + Cos +

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SLIDE 17
  • Do not need to have a right angle
  • Do need to have at least one matching pair (angle and
  • pposite side)
  • Always check for a second solution.
  • Label your diagram and rewrite the Sine formula using

these labels.

  • Formula is on page 16 of log book

Sine Rule

Page 16

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SLIDE 18
  • Do not need a right angle.
  • Do need two sides with the angle in between (SAS).
  • Rewrite the formula using your labels.
  • Formula on page 16 of log book

Cosine Rule

Page 16

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SLIDE 19
  • https://web.actuaries.ie/students/maths-tutorials-higher-level-leaving-certificate-20192020
  • 18th November 2019
  • Same location
  • 6 - 8 pm
  • Topic

Next Tutorial

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