Trigonometric Identities

Trigonometric Identities

sin2(x) = 1 - cos(2x) 2

cos2(x) = 1 + cos(2x) 2

Reduction Formulas

sinn(x)dx

=

sinn-1(x) -

cos(x)

+

n

-

1

sinn-2(x)dx

n

n

cosn(x)dx = cosn-1(x) sin(x) + n - 1 cosn-2(x)dx

n

n

tann(x)dx = tann-1(x) - tann-2(x)dx n-1

cotn(x)dx

=

cotn-1(x) -

-

cotn-2(x)dx

n-1

secn(x)dx = tan(x) secn-2(x) + n - 2 secn-2(x)dx

n-1

n-1

cscn(x)dx

=

cot(x) -

cscn-2(x)

+

n

-

2

cscn-2(x)dx

n-1

n-1

Other Integration Formulas

dx

1

x

x2

+

a

=

a

arctan

a

+C

Important Power Series

(for a > 0)

1

= xk = 1 + x + x2 + x3 + . . .

1-x

k=0

ex =

xk

x2 x3 = 1+x+ + +...

k!

26

k=0

(-1)kx2k+1

x3 x5

x7

sin(x) =

=x- + -

+...

(2k + 1)!

6 120 5040

k=0

(-1)kx2k

x2 x4 x6

cos(x) =

= 1- + - +...

(2k)!

2 24 720

k=0

xk

x2 x3 x4

ln(1 - x) =

= x + + + + . . . arctan(x)

k

234

k=1

(-1)kx2k+1

x3 x5 x7

=

= x- + - +...

2k + 1

357

k=0

Differential Eqauations

dy = k(y - b)

dt

dy

y

= ky 1 -

dt

A

y(t) = Cekt + b A

y(t) = 1 - Ce-kt (nonequilibrium)

 ................
................

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

Google Online Preview   Download