1. CIE Centre A-level Pure Maths
P1 Chapter 18
CIE Centre A-level Pure Maths
© Adam Gibson

2. RADIANS
The radian is useful to distinguish between quantities of
different nature but the same dimension.
For example angular velocity can be measured in
radians per second (rad/s).
The angle subtended at the center of a circle by an arc
of circumference equal in length to the radius of the circle
is one radian. Angle measures in radians are often given
without any explicit unit. When a unit is given, sometimes
the abbreviation rad is used
There are 2π (approximately ) radians
in a complete circle.

3. RADIANS
How can we convert between
radians and degrees? or
Using this conversion, find:
1 degree in radians = …
1 radian in degrees =

4. Finding areas and arc lengths
The ratio of the arc
length to the circumference
is the same as the ratio
of the angle to 360 deg. A s θ r
Can we use the same idea to find the area A … ?
Remember these
formulae – but
only with radians!

5. Why measure angles in radians?
Here is one reason (there are others … ).
Suppose we want to calculate the first derivative
of y = sinx at x = 0.
We don’t have a simple formula, so let’s use the definition
of derivative (limits):
Put x = 0. What
happens?

6. Why measure angles in radians?
“arc”
“chord” P r O θ A Q

7. Why measure angles in radians?
Later, we will discuss the formula:
which works only
in radians.
Now you should read carefully Example on p. 266
and then do:
Exercise 18A Q1 a,e,i Q2 a,e,i Q5, Q8, Q10