M5.3.2 For the adult
The unit circle and any angle
How can I find sin 150° or cos 225° when the angle does not fit in a right angled triangle?
What this chapter teaches
The unit circle has radius 1. Turning through any angle θ from the point (1, 0) reaches the point (cos θ, sin θ). So sin is the height and cos is the horizontal distance, and both can be negative. The sign of each ratio depends on the quadrant, and the size comes from the acute reference angle.
Three questions to ask
There is no one right wording. Listen for the idea.
- Where is the point on the unit circle after turning 150° from (1, 0), and is its height positive or negative?
- Why is tan 90° not defined?
- How do you find sin 210° from sin 30°?
After the chapter, the learner can
- Use the unit circle to find sin and cos of any angle
- Find the sign of sin, cos and tan in each quarter
What they copy into their notebook
P = (cos θ, sin θ) on the unit circle. Signs: first All, second Sin, third Tan, fourth Cos. Size from the reference angle. tan θ = sin θ ÷ cos θ, none when cos θ = 0.