AP CALCULUS PREREQUISITES
Trigonometry Identities
Sum and Difference Identities
sin (" ± ! ) = sin " cos ! ± cos " sin !
cos(" ± ! ) = cos " cos ! m sin " sin !
r
Other Identities
y
x
y
r
x
cos ! =
r
y
tan ! =
x
sin ! =
r
y
r
sec ! =
x
x
cot ! =
y
csc ! =
1
sin !
1
sec ! =
cos !
1
cot ! =
tan !
csc ! =
Quotient Identities
tan ! =
sin !
cos !
1 " cos 2!
2
1 + cos 2!
cos 2 ! =
2
sin 2 ! =
cot ! =
Unit Circle
Cos = x
Sin = y
y
Tan =
x
cos !
sin !
Pythagorean Identities
sin 2 ! + cos 2 ! = 1
tan 2 ! + 1 = sec 2 !
1 + cot 2 ! = csc 2 !
Double-Angle Identities
sin 2! = 2 sin ! cos !
cos 2! = cos 2 ! " sin 2 !
cos 2" = 2 cos 2 " ! 1
cos 2! = 1 " 2 sin 2 !
Conversion between Radians and
Degrees
180
!
!
Degrees to Radians x
180
Radians to degrees x
Exponents
Logarithms
x0 = 1
x a ! x b = x a +b
xa
= x a !b
b
x
a b
(x ) = x
x1 = x
ab
x !a =
1
xa
a
b
x = b xa
log(ab ) = log a + log b
ln 1 = 0
'a$
log% " = log a ! log b
ln e = 1
&b#
log(a b )= b log a
ln e x = x
log 1 = 0
e ln x = x
log b b = 1
Note: You cannot take the logarithm of zero or
a negative number.
Geometry
1
bh
2
Area of a rectangle = bh
1
Area of a trapezoid = h(b1 + b2 )
2
2
Area of a circle = ! r
Area of a triangle =
Circumference of a circle = 2! r
Pythagorean Theorem (right triangles only) = a 2 + b 2 = c 2
Volume of a right circular cylinder = ! r 2 h
Surface area of a right circular cylinder = 2! rh
Volume of a right circular cone =
Volume of a sphere =
4
! r3
3
Surface area of a sphere = 4! r 2
1
! r 2h
3