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 • www.themathstutor.ie • Normally €99.99 • Discount code: SAI • €49.50 for the year • Access to June 2020
Material from tonight • 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
What can you expect to get from tonight? • Radians & Degrees • Sine Rule • Length of an Arc • Area of a triangle • Trigonometric ratios • Cosine rule • Unit circle • 3D Questions
Exam Technique: • 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.
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
Trigonometric Ratios 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?
Page 16 Trigonometric Ratios Sin e, Cos ine and Tan gent are well known but are given on page Page 13 16 of your Formulae book – along with Pythagoras’ Theorem. Cosec ant, Sec ant and Cot angent are the reciprocals of these and are given on page 13.
Trigonometric Ratios
Trigonometric Ratios Handy way to remember the ratios: 𝑷𝑞𝑞𝑝𝑡𝑗𝑢𝑓 𝑰𝑧𝑞𝑝𝑢𝑓𝑜𝑣𝑡𝑓 𝑼𝑏𝑜 𝑦 = 𝑷𝑞𝑞𝑝𝑡𝑗𝑢𝑓 𝑩𝑒𝑘𝑏𝑑𝑓𝑜𝑢 𝐓in 𝑦 = 𝑰𝑧𝑞𝑝𝑢𝑓𝑜𝑣𝑡𝑓 𝐃os 𝑦 = 𝑩𝑒𝑘𝑏𝑑𝑓𝑜𝑢 SOH CAH TOA S illy O ld H arry C aught A H erring T rawling O ff A merica
Page 13 Beyond the right-angled triangle: 90° θ ° = x° θ ° = 180° - x° 2 nd 1 st Sin + All + Quadrant Quadrant 0° 180° 360° Tan + Cos + 3 rd 4 th Quadrant Quadrant θ ° = 180° + x° θ ° = 360° - x° 270°
Page 16 Sine Rule • 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
Page 16 Cosine Rule • 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
Next Tutorial • https://web.actuaries.ie/students/maths-tutorials-higher-level-leaving-certificate-20192020 • 18 th November 2019 • Same location • 6 - 8 pm • Topic 19
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