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Trigonometry Review
Angle Measurement
360   2 radians, so 180   radians
To convert from degrees to radians, multiply by
To convert from radians to degrees, multiply by

180
180

.
.
Special Angles
2
3

 120
3 
 135
4
5  150
6

  180

2
 90


0
r=1
3 / 2  270
 60
3
  45
4
  30
6


Special Angles - Unit Circle Coordinates
 1 , 3 


2
2


 1 , 1 


2
2

 3 , 1 


2
2


 1,0
0,1
1

3
,
 2

2


π/2
3π/4
π/3
2π/3
π/4
5π/6
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
sin 2  2 sin cos
cos 2  cos   sin 
2
2
 2 cos   1
2
 1  2 sin 2 
Inverse Trig Functions
y  sin1 x  arcsin x is equivalent to x  sin y
y  cos 1 x  arccos x 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