Download Trigonometric Formulas

Trigonometric Formulas
Definitions of trigonometric functions on the unit circle ( x 2  y 2  1 ):
cos t  x
sin t  y
tan t  y / x , x  0
csc t  1 / y , y  0
cot t  x / y , y  0
sec t  1/ x , x  0
Definitions of trigonometric functions on the right triangle:
opposite
adjacent
sin  
tan  
cos  
hypotenuse
hypotenuse
hypotenuse
hypotenuse
csc  
sec  
cot  
opposite
adjacent
Reciprocal relations:
csc t  1/ sin t
tan t  sin t / cos t
Even-Odd properties:
sin  t    sin t (odd)
csc t    csc t (odd)
Pythagorean identities:
sin 2 t  cos 2 t  1
cos t   cos t (even)
sec t    sec t (even)
tan 2 t  1  sec 2 t
To convert degrees to radians, multiply by
Co-function identities:
sin    cos 90   

tan    cot 90
sec   csc90






180
tan  t    tan t (odd)
cot t    cot t (odd)
1  cot 2 t  csc 2 t
. To convert radians to degrees, multiply by

cot    tan 90
csc   sec90



cos   sin 90   
Addition and Subtraction formulas:
sin s  t   sin s cost   coss sin t 
coss  t   coss cost   sin s sin t 
tan s   tan t  sin s  t 
tan s  t  

1  tan s  tan t  coss  t 
Double Angle formulas:
sin 2x  2 sin xcosx
cot t  1/ tan t
cot t  cos t / sin t
sec t  1/ cos t
Angle Conversions:
opposite
adjacent
adjacent
opposite


sin s  t   sin s cost   coss sin t 
coss  t   coss cost   sin s sin t 
tan s   tan t  sin s  t 
tan s  t  

1  tan s  tan t  coss  t 
cos2 x   cos 2 x   sin 2 x   1  2 sin 2 x   2 cos 2 x   1
2 tan x 
sin 2 x 
tan 2 x  

2
1  tan  x  cos2 x 
180

.