Transcript Document

Trigonometry Review
Angle Measurement
360  2 radians, so 180   radians

.
To convert from degrees to radians, multiply by
180
To convert from radians to degrees, multiply by
180

.
Special Angles
2
3

2
 120
3 
 135
4
5  150
6

  180

 90


 60
3
  45
4
  30
6

0
r=1
3 / 2  270

Special Angles - Unit Circle Coordinates
 1

3

,


2
2


0,1
 1 , 1 


2
2


3π/4
2π/3


3
1
, 

2
2
5π/6

 1,0
1

3
,
 2

2


π/2
π/3
π/4
π/6
0
π
3π/2
0 ,1
r=1
 1 , 1 


2
2


 3

1
,


2
2


1,0
Trig Functions - Definitions
y
sin  
r
r
csc  
y
x
cos 
r
r
sec  
x
y
tan 
x
x
cot 
y
r

r
(x,y)
x y
2
2
Trig Functions - Definitions
opp
sin  
hyp
adj
cos 
hyp
opp
tan 
adj
hyp
opp

adj
Trig Functions - Definitions
opp
sin  
hyp
hyp
csc  
opp
adj
cos 
hyp
hyp
sec  
adj
opp
tan 
adj
adj
cot 
opp
Trig Functions
Signs by quadrants
sin, csc positive
tan, cot positive
all functions positive
cos, sec positive
Trig Identities
Reciprocal
1
csc  
sin 
1
sec  
cos
1
cot 
tan
Quotient
sin 
tan 
cos
cos
cot 
sin 
Trig Identities
Pythagorean
sin   cos   1
2
2
tan   1  sec 
2
2
1  cot   csc 
2
2
Trig Identities
Double Angle
sin2  2 sin cos
cos 2  cos   sin 
2
2
 2 cos   1
2
 1  2 sin2 
Inverse Trig Functions
y  sin1 x  arcsin x is equivalent to x  sin y
y  cos1 x  arccosx is equivalent to x  cos y
Solving Trig Equations
Use algebra, then inverse trig functions or knowledge
of special angles to solve.
1
example: if sin  
2
0    2