Download Definition of the Six Trigonometric Functions

Definition of the Six Trigonometric Functions

2
opp.
hyp.
sin  
csc 
opp.
hyp.
adj.
hyp.
cos  
sec  
hyp.
adj.
opp.
adj.
tan  
cot  
adj.
opp.
Right triangle definitions, where 0 <  <
Hypotenuse
Opposite

Adjacent
Circular function definitions, where  is any angle.
y
y
sin  
csc  
r
r  x2  y2
x
cos  
sec  
(x,y)
r
r
θ
y
y
x tan  
cot  
x
x
Reciprocal Identities
1
1
sin u 
cos u 
csc u
sec u
1
1
csc u 
sec u 
sin u
cos u
r
y
r
x
x
y
Negative Angle Identities
1
cot u
1
cot u 
tan u
tan u 
Tangent and Cotangent Identities
sin u
cos u
tan u 
cot u 
cos u
sin u
Pythagorean Identities
sin 2 u  cos 2 u  1
1  tan 2 u  sec 2 u
1  cot 2 u  csc 2 u
Cofunction Identities




sin   u   cos u
cos  u   sin u
2

2





csc  u   sec u
sec  u   csc u
2

2





tan   u   cot u
cot  u   tan u
2

2

sin( u )   sin u
csc( u )   csc u
cos(u )  cos u
sec( u )  sec u
cot( u )   cot u
tan( u )   tan u
Sum and Difference Formulas
sin( u  v)  sin u cos v  cos u sin v
cos(u  v)  cos u cos v  sin u sin v
tan u  tan v
tan( u  v) 
1  tan u tan v
Half Angle Identities
1  cos u
u
sin    
2
2
1  cos u
u
cos   
2
2
1  cos u
u
tan    
1  cos u
2