Trigonometry 1

11th November 2019

• Trigonometry 1

• Question Focused Approach

• 2 hours - 10mins break at 7pm

• Feedback form after the break

• Any questions? – Just Ask!!

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Useful Resource for Project Maths

• 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

• 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

• Read the question carefully.

• Know the vocabulary.

• Draw a diagram every time.

• Label all diagrams.

Exam Technique:

• 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:

• Know how to round your answer.

• Know when to round your answer.

• Do not round early.

Exam Technique:

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.

Definition of a Radian

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

Page

13

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

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

Trigonometric Ratios

Handy way to remember the ratios:

𝐒in 𝑥 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒𝐂os 𝑥 =

𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒𝑻𝑎𝑛 𝑥 =

𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

SOH CAH TOA

Silly Old Harry Caught A Herring Trawling Off America

Trigonometric Ratios

Beyond the right-angled triangle:

2nd

Quadrant1st

Quadrant

3rd

Quadrant4th

Quadrant

0°

90°

180°

270°

360°

θ° = x°θ° = 180° - x°

θ° = 180° + x° θ° = 360° - x°

Page

13

Sin + All +

Tan + Cos +

• Do not need to have a right angle

• Do need to have at least one matching pair (angle and opposite 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

• 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

• https://web.actuaries.ie/students/maths-tutorials-higher-level-leaving-certificate-20192020

• 18th November 2019

• Same location

• 6 - 8 pm

• Topic

Next Tutorial

19