Transcript Trig – In a Nutshell

Trig – In a Nutshell
Help I’m trapped in a nutshell
The Unit Circle
(0,1)
+,+
-,+
(1,0)
(-1,0)
+,-
-,(0,-1)

2
+

θ
-
3
2
2
These are the reference triangles
1
30  
1
1
2
6
45  
2
2
4
2
2
3
2
3
2
1
60  
3
1
2
Trigonometric Functions
r
y
θ
x
opp y
sin  

hyp r
1
hyp r
csc  


sin  opp y
adj x
cos  

hyp r
sec  
sin  opp y
tan  


cos  adj x
1
cos  adj x
cot  



tan  sin  opp y
1
hyp r


cos  adj x
Conversion
Radians to Degrees:
Radians 
180

5
12
Degrees to Radians:
130
Degrees 

180
Lets quickly review

30 
6

45 
4

60 
3

90 
2
5
6
3
4
5
3
3
2
150
135
300
270
Examples
5
1. Find sin
6
1
2
150
What Quadrant? Q II
Pull out Triangle
150
1/2
60
1
30
Draw down
side to x-axis
 3
2
What Happens if…
If you land on an axis, there is no triangle. So
instead of using sides of the triangle, use x, y and
r. Unless otherwise specified, r = 1.
1. Find sin π, cos π and tan π.
y 0
sin     0 What would csc be?
r 1
x 1
cos     1
r 1
y 0
tan     0
x 1
(-1,0)
Examples
3
1. If sin x  and x is in QII find all six Trig Functions
5
Examples
Find the values of the six trig. functions of , if  is an angle
in standard position with the point (4 , 3) on its terminal ray.