PRE-CALCULUS GRADE 12 FORMULA PAGE
The following information may be useful when writing this examination.
Trigonometry
Algebra
a = rθ
csc θ =
cot θ =
For ax 2 + bx + c = 0 , x =
1
sin θ
sec θ =
1
tan θ
tan θ =
sin θ
cos θ
cot θ =
cos θ
sin θ
sin 2 θ + cos 2 θ = 1
1
cos θ
−b ± b 2 − 4ac
2a
Logarithms
In chemistry, the pH scale measures
the acidity (0–7) or alkalinity (7–14)
of a solution. It is a logarithmic scale
in base 10. Thus, a pH of 9 is 10 times
more alkaline than a pH of 8.
pH Scale
tan 2 θ + 1 = sec 2 θ
increasing
acidity
increasing
alkalinity
1 + cot 2 θ = csc 2 θ
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
sin (α + β ) = sin α cos β + cos α sin β
neutral water
sin (α − β ) = sin α cos β − cos α sin β
Permutations and Combinations
cos (α + β ) = cos α cos β − sin α sin β
n Pr
cos (α − β ) = cos α cos β + sin α sin β
tan (α + β ) =
tan (α − β ) =
tan α + tan β
1 − tan α + tan β
tan α − tan β
1 + tan α tan β
n Cr
=
=
n!
( n − r )!
(nr) = r !(nn!− r )!
In the expansion of ( a + b )n ,
the general term is
t k +1 = nC k a n − k b k
sin 2θ = 2 sin θ cos θ
cos 2θ = cos 2 θ − sin 2 θ
= 2 cos 2 θ − 1
= 1 − 2 sin 2 θ
tan 2θ =
2 tan θ
1 − tan 2 θ
Pre-Caculus 12 – Formula Page
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ROUGH WORK SPACE FOR GRAPHING
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Pre-Caculus 12 – Formula Page