Review Handout For Math 1220

Review Handout For Math 1220

Logarithms

Suppose u and b are positive numbers and b = 1.

logb u is the power of b which gives u: p = logb u u = bp. Suppose u, v, a and b are positive numbers with a = 1

and b = 1, and p is any real number.

log u = log10 u , ln u = loge u logb 1 = 0 , logb b = 1

loga u

=

logb u logb a

logb u = logb v = u = v

logb up = p logb u logb uv = logb u + logb v

blogb u = u

logb

u v

=

logb

u

-

logb

v

Inverse Trigonometric Functions

For

|x|

1,

sin-1 x

is

the

angle

such

that

-

2

2

and

sin

= x.

For |x| 1, cos-1 x is the angle such that 0 and cos = x.

For

any

real

number

x,

tan-1 x

is

the

angle

such

that

-

2

<

<

2

and

tan

=

x.

For any real number x, cot-1 x is the angle such that 0 < < and cot = x.

For

|x|

1,

sec-1 x

is

the

angle

such

that

0

<

2

or

<

3 2

and

sec

=

x.

For

|x|

1,

csc-1 x

is

the

angle

such

that

0

<

2

or

<

3 2

and

csc

=

x.

For - 1 x 1 , sin(sin-1 x) = x

For

-

2

x

2

,

sin-1(sin x) = x

For - 1 x 1 , cos(cos-1 x) = x

For 0 x , cos-1(cos x) = x

For any real number x, tan(tan-1 x) = x For any real number x, cot(cot-1 x) = x

For

-

2

<

x

<

2

,

tan-1(tan x) = x

For 0 < x < , cot-1(cot x) = x

For x -1 or x 1, sec(sec-1 x) = x For x -1 or x 1, csc(csc-1 x) = x

For

0x<

2

or

x<

3 2

,

sec-1(sec x) = x

For

0 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download