Trigonometry Formulas
These four pages are permitted on the proctored final for Trig. Do not
add any other notes to these pages! The proctor has been told to
check the front and back of each page against his/her copy to make
sure you have not added anything to these pages. If there are any
additions, you will receive an F for cheating. Saying you did not
understand the rules is not an excuse!
Formulas you need to Memorize:
You are responsible for knowing all other formulas not given below.
A few examples of formulas you need to know are:
Law of Cosines & Sines.
All formulas to find the area of a triangle.
Polar coordinate formulas from 8.5.
Sum & Difference Formulas:
Half Angle Formulas:
cos(A + B)
1  cos(A)
A
sin    
2
2
= cos(A)cos(B) – sin(A)sin(B)
1  cos(A)
A
cos    
2
2
cos(A - B)
= cos(A)cos(B) + sin(A)sin(B)
 A  1  cos(A)
tan   
sin(A)
2
sin(A + B)
= sin(A)cos(B) + cos(A)sin(B)

sin(A)
1  cos(A)
sin(A - B)
= sin(A)cos(B) - cos(A)sin(B)
tan(A  B) 
tan(A  B) 
tan(A)  tan(B)
1  tan(A) tan(B)
tan(A)  tan(B)
1  tan(A) tan(B)
Product Sum Formulas:
(Trig Students Only)
x  y
x  y
sin(x)  sin(y)  2sin 
 cos 

 2 
 2 
x  y
x  y
sin(x)  sin(y)  2sin 
 cos 

 2 
 2 
Double Angle Formulas:
sin(2A) = 2sin(A)cos(A)
cos(2A) = cos2(A) – sin2(A)
= 2cos2(A) – 1
= 1 – 2sin2(A)
x  y
x  y
cos(x)  cos(y)  2cos 
 cos 

 2 
 2 
x  y x  y
 sin 

 2   2 
cos(x)  cos(y)   2 sin 
tan(2A) 
2 tan(A)
1  tan2 (A)
Theorem:
(Trig Students Only)
Law of Sines ambiguous
case:
Asin(x) + Bcos(x) = ksin(x +),
A is obtuse: a < b: No solution
a > b: One solution
where k 
sin() 
B
,
k
A 2  B2
cos() 
A
k
Complex Number Formula:
(Trig Students Only)
z1 = r1[cos(1) + isin(1)],
z2 = r2[cos(2) + isin(2)]
z1z2
= r1r2[cos(1 + 2) + isin(1 + 2)]
z1 r1
 cos(1  2 )  isin(1  2 )
z2 r2
zn = rn[cos(n()) + isin(n())]
1
1

   360o k 
   360o k  
i
sin




n
n





where k = 0, 1, 2, …, n - 1
z n  r n cos 
A is acute: a < h:
No solution
a = h:
One solution
a > b:
One solution
h < a < b: Two solutions
Vectors:
|v|
 q1  p1 
2
  q2  p2 

PQ   q1  p1, q2  p2 
  v1 ,v 2   v
cos    
uv
| u || v |
2
Points of Special Interest on the Unit Circle: