Download Unit 5: Trigonometric Functions

Unit 5: Trigonometry I (Day 1)
Radian Measure
Consider a circle of radius 1 (called a unit circle).
i) How long is the arc contained by an angle of 90o?
ii) 180o?
iii) How many degrees is the angle containing an arc of length 2.5?
Definition:
1 radian is the measure of an angle containing an arc of length r in a circle of
radius r.
To convert between degrees and radians:   180 o
Similarly, 2  360 o
Degrees  Radians: Multiply by
Radians  Degrees: Multiply by

180 o
180 o

Examples:
Convert from degrees to radians:
i) 30o
ii) 90o
iii) 45o
iv) 110o
v) 360o
v) 270o
* We often leave radians in terms of 
** The units for radians are either: ‘radians’ or nothing.
If an angle measures 2 , no units included, then we are working in radians.
Convert from radians to degrees.
i) 1 radian
iii)
ii) 5.6 radians
5
6
iv)
3
4
Finding the length of an arc in a circle of radius r:
1. Determine the fraction of the circle being worked with.
2. Multiply this by the circumference
Degrees: Arc length = a 
Radians: Arc length = a 

360o
 2r

 2r
2
Examples:
i) A circle has radius 8 cm. Calculate the length of the arc subtended by each
angle:
a) 2.3 radians
b) 75o
ii) A circle has radius 5 cm. Find the angle at the center containing an arc
length of:
a) 6 cm (in degrees)
b) 15 cm (in radians)
ex: A bicycle wheel has a radius of 30 cm. What is the distance rolled if the
wheel has turned:
45o
120o
1000o
Homework:
p. 485 #1-4
p. 494 #5, 8, 9