Measuring Angles – Radian Measure

Given circle of radius r, a radian is the measure of a central angle subtended by an arc length s equal to r.

The radian measure of an arbitrary angle

There are radians in a angle. Why?

s

r

s

r

2 360

Using Radian Measure

1. Degree 2 Radian conversions:

2. Measuring angles as fractions of3. Common angles

4. Finding arc lengths and sector areas using proportions!

180degrees radians

180 radians

902radians

306radians

45

4radians

60

3radians

2

2sectorArea r

s r

SOH-CAH-TOA

Let be an acute angle in right triangle

ABC

sinopp

hyp

cosadj

hyp

tanopp

adj

cschyp

opp

sechyp

adj

cotadj

opp

A

B

C

opposite

adjacent

hypoteneuse

Two Famous Triangles

isosceles 45-45-90

equilateral 30-60-90

1

1

1

2

2 23

4

4

6

3

Know how to do the following

1. Using the famous triangles derive the 6 trig functions for

2. Given any two sides of a right triangle find the values of all six trig. functions

3. Given a side and an angle solve the right triangle (i.e. determine the missing lengths)

4. Given the value of one trig. function, determine the values of the other five

, ,6 4 3and

Some Miscellaneous Stuff

1. Angular velocity in radians per unit time

2. Alternate area formula for a triangle

3. Complementary angles & co-functions

t

1sin

2Area a b

a

b sinh b

2cosine sine