Download Measuring Angles * Radian Measure

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.
s

r
s
The radian measure of an arbitrary angle  
r
There are 2 radians in a 360 angle. Why?
Using Radian Measure
 degrees
 radians

1. Degree 2 Radian conversions:
180

2. Measuring angles as fractions of 
3. Common angles 180   radians

90  radians
2


60  radians 45  radians 30   radians
3
4
6
4. Finding arc lengths
and sector areas
using proportions!

s  r
Areasector 

2
r2
SOH-CAH-TOA
Let  be an acute angle
in right triangle  ABC
B
hypoteneuse
A

adjacent
opp
sin   
hyp
hyp
csc   
opp
adj
cos   
hyp
hyp
sec   
adj
opp
tan   
adj
adj
cot   
opp
opposite
C
Two Famous Triangles
isosceles
45-45-90

1
2
4

4
1
equilateral
30-60-90

2
6
2
3

1
3
Know how to do the following
1. Using the famous triangles derive the 6 trig
functions for  6 , 4 , and  3
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
Some Miscellaneous Stuff
1. Angular velocity in radians per unit time


t
2. Alternate area formula for a triangle
1
Area  a  b  sin  
2
b
h  b  sin  

a
3. Complementary angles & co-functions

cosine    sine 
2

