AS Core Maths - TAM Online Session 8: Trigonometry

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Presentation transcript:

AS Core Maths - TAM Online Session 8: Trigonometry A warm-up question: The diagram shows two circles, the radius of the larger one being the diameter of the smaller one. Prove that the arc lengths AB and A’B’ are equal.

Session Content Basic trigonometry Graphs of trig functions Solving trig equations Transformations Radians Arcs & sectors NB: This is content based on chapter 10 in the AS core textbook

GCSE recap: Exact values 0° 30° 45° 60° 90° sin 𝜃 cos 𝜃 tan 𝜃

GCSE recap: Area of a triangle & the sine rule

GCSE recap: The cosine rule

How long do you think x is? 6 cm 8 cm 40º x Not to scale

The ambiguous case

Why does my calculator say that sin 150 is 0 Why does my calculator say that sin 150 is 0.5 when you can’t have a right-angled triangle with an angle of 150?

Extending the domain: circular functions

Trigonometric identities

If x is obtuse and sin x =0.4, find cos x and tan x Question If x is obtuse and sin x =0.4, find cos x and tan x

Core 2 Jun 07 - Q8 [5 marks]

Transformations

Transformations In each case, the red graph is y=sinx

Find the equations

Radians

Radians and degrees

Arc length and area of sector

Arcs and Sectors exam style questions 1. Core 2 Jan 10 - Q4 [3 marks] A sector of a circle has area 8.45cm2 and sector angle 0.4 radians. Calculate the radius of the sector. 2. Core 2 May 09 - Q4 [4 marks] A sector of a circle of radius 18.0cm has arc length 43.2cm. (i) Find in radians the angle of the sector. (ii) Find this angle in degrees, giving your answer to the nearest degree.

The diagram shows two circles, the radius of the larger one being the diameter of the smaller one. Prove that the arc lengths AB and A’B’ are equal.

Session content check Basic trigonometry Graphs of trig functions Solving trig equations Transformations Radians Arcs & sectors

MEI Core 2 May 09 - Q5 [5 marks ]

AQA Core 2 - Jan 12, Q8 [10 marks]

MEI Core 2 Jan 09 - Q4 [3 marks] Solve the equation 𝑠𝑖𝑛2𝑥=−0.5 for 0°<𝑥<180°

MEI Core 2 Jan 09 - Q11(i) [6 marks]

MEI Core 2 Jan 09 - Q11(ii) [6 marks]

MEI Core 2 Jun 08 - Q7 [5 marks]

Edexcel Core 2 - Jun 11, Q5 [7 marks]

OCR Core 2 Jun 11 - Q9 [11 marks]