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Topic 4: Trigonometric functions

Circular measure and radian measure

2 hours

• Define and use radian measure and understand its relationship with degree measure. 1 interactive
• Calculate lengths of arcs and areas of sectors in circles.

Introduction to trigonometric functions

8 hours

• Understand the unit circle definition of cos(𝜃), sin(𝜃) and tan(𝜃) and periodicity using radians. 1 interactive
• Understand and use the exact values of cos(𝜃), sin(𝜃) and tan(𝜃) at integer multiples of π 6 and π 4.
• Sketch the graphs of 𝑦 = sin(𝑥), 𝑦 = cos(𝑥) and 𝑦 = tan(𝑥) on extended domains.
• Recognise and determine the effect of the parameters 𝑎, 𝑏, ℎ and 𝑘 on the graphs of 𝑦 = 𝑎 sin(𝑏(𝑥 − ℎ))+ 𝑘, 𝑦 = 𝑎 cos(𝑏(𝑥 − ℎ))+ 𝑘, with and without technology. 1 interactive
• Sketch the graphs of 𝑦 = 𝑎 sin(𝑏(𝑥 − ℎ))+ 𝑘, 𝑦 = 𝑎 cos(𝑏(𝑥 − ℎ)) + 𝑘, with and without technology.
• Solve trigonometric equations, with and without technology, including the use of the Pythagorean identity sin2(𝐴)+ cos2(𝐴) = 1.
• Model and solve problems that involve trigonometric functions, with and without technology.