In this task (question 4), you will use logic to investigate the creation of shapes from circles. You will be assessed using criterion B (Investigating patterns) and criterion C (Communication).
Describe patterns and find general rules in arc lengths and angles.
In a unit circle, angle is increased by 15∘ at each stage starting from 0∘ as shown in the following table.
Stage (n)
Angle (in degrees)
1
0
2
15
3
30
4
45
The pattern between the different stages (n) and arc length (A) is observed.
Q 7.1 Write down the missing values in the table.
Stage (n)
Arc Length (A)
1
0
2
3
4
Q 7.2 Describe in words a pattern for A.
Q 7.3 Write down a general rule for A in terms of n.
Q 7.4 Consider a circle with radius 4 units. Investigate the relationship between the stage number n and B. In your answer:
- predict values in the table.
- determine a rule for B in terms of n.
- verify your rule for B.
- justify your rule for B.
- show your working clearly.