Arc length, sector area and shaded regions
Watch the whole lecture free
Make a free account to watch every lecture to the end: 2 worked examples, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 2 worked examples, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Why mathematicians chose radians
- Degrees and radians
Read the transcript of the teaching part
Last time
Before we start: last time, in Tangents to a circle and a line and a circle, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Why mathematicians chose radians
Degrees come from the Babylonians, who liked the number three hundred and sixty. Radians come from the circle itself. One radian is the angle where the arc is as long as the radius. That makes the formulas for arcs and sectors beautifully short.
Degrees and radians
A half turn is one hundred and eighty degrees, which is pi radians. To change degrees to radians, multiply by pi over one hundred and eighty. Sixty degrees is pi over three. Thirty is pi over six. Ninety is pi over two. Keep pi in exact answers. Set your calculator to radians when a question gives pi.
Chapter 9: Circular measure
- Arc length, sector area and shaded regions 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.