FORMULA SHEET

P  P0c et
P  P0 (2)
et
dt
P  P0 (0.5)
et
ht
 b  b2  4ac
x
2a
radians  180o
a  r
period 
b
2
b
2
period
y  a cos bx  c  d
y  a sin bx  c  d
y  a cos 2
x  c   d
y  a sin 2
x  c   d
p
p
Trigonometric Identities
A trigonometric identity is an equation involving trigonometric functions that is true for all permissible
values of the variable. Trigonometric identities can be verified numerically and graphically, but this is not
sufficient to conclude that an equation is an identity. This can only be done through algebraic proof. Also,
trigonometric expressions can be used to simplify more complicated trigonometric expressions and to
determine exact trigonometric values for some angles.
Reciprocal Identities
Quotient Identities
Pythagorean Identities
csc x 
1
sin x
tan x 
sin x
cos x
cos2 x  sin2 x  1
sec x 
1
cos x
cot x 
cos x
sin x
1 tan2 x  sec2 x
cot x 
1
tan x
cot2 x  1  csc2 x
Sum Identities
Difference Identities
sin
 A  B   sin
cos
 A  B   cos
tan
 A  B 
A cos B  cos A sin B
A cos B  sin A sin B
tan A  tan B
1  tan A tan B
sin
 A  B   sin
cos
 A  B   cos
tan
 A  B 
A cos B  cos A sin B
A cos B  sin A sin B
tan A  tan B
1  tan A tan B
Double-Angle Identities
sin 2A  2 sin A cos A
cos 2A  cos2 A  sin2 A
tan 2 A 
2 tan A
1  tan2 A
cos 2A  2 cos2 A  1
cos 2A  1 2 sin2 A
Proving Trigonometric Identities
 To prove a trigonometric identity algebraically, simplify both sides of the identity separately into identical
expressions.
 Do not move terms from one side of the identity to the other.
 It is usually easier to make a more complicated expression easier than to make a simple expression more
complicated. Consider changing the UGLY SIDE FIRST
Some strategies that can be used when proving identities are: (TIPS)

Use known quantities to make substitutions.

If quadratics are present, the Pythagorean identity, or one of its alternate forms, can often be used.

Rewrite each expression using sine and cosine only.

Multiply the numerator and the denominator by the conjugate of an expression.

Factor to simplify expressions.
"Q.E.D." is an abbreviation for the Latin phrase "quod erat demonstrandum"
("that which was to be demonstrated"), a notation which is placed at the end of a mathematical proof to indicate its
completion.