Honors Precalculus Formula Sheet PDF

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C2.0 Honors Precalculus Progress Check Formula Sheet Trigonometric Identities: sin 2   cos 2   1

sec2   1  tan2 

csc2   1  cot2 

sin      sin  cos   cos sin  sin  2   2sin  cos tan     

cos      cos  cos 



cos 2   cos2   sin2   2cos2   1  1 2sin2 

tan  tan  1 n 1  cos    cos     2 2 

1  cos  sin     2  2 Triangle Formulas:

Law of Sines: sin A  sin B  sin C a

b

Law of Cosines: c2  a2  b2  2 ab cos C

c

Area of a Triangle: 1 ab sin C 2

Parametric Equations for Projectile Motion (distances in feet): x   vo cos   t y  16t 2   v o sin   t  h o

Vectors: If u

1

u

2

, then

1

 u 22 with direction angle tan  1

Dot Product of Two Vectors in the Plane u

Angle Between Two Vectors u

1

u  u

u2 , placed in the appropriate quadrant. u1 2

1



.

2

2 2

Series: Arithmetic Sequence and Series:  2a1   n  1 d   a  an  Sn  n  1  n   2  2   

an  a1   n  1 d Geometric Sequences and Series:

 1 r n  S n  a1    1 r 

an  a1r n 1

Sum of an Infinite Geometric Series: S  a1 , r  1 1 r

Counting: Permutations:

n

Pr 

n! n  r !

Combinations:

n

Cr 

n! r! n  r !

Binomial Theorem:

 n  n  n  n1  n n 2 2  n  n  n a    a b   a b  ...   a n rb r  ...  b n ,where    nCr  0  1  2  r  n  r

 a  b n  

OR

x  y 

n

n

 x  nx

n 1

y

n  n 1 1 2

x

n 2

y  2

n  n 1  n  2  1 2 3

x

n 3

n

n! n r r x y r 0 r ! n  r  !

y  ...  y   3

n...