WZORY TRYGONOMETRYCZNE - UTP

[Pages:1]WZORY TRYGONOMETRYCZNE

tg x

=

sin x cos x

ctg x

=

cos x sin x

sin 2x = 2 sin x cos x

cos 2x = cos2 x - sin2 x

sin2 x

=

1-cos 2x 2

cos2

x

=

1+cos 2x 2

sin2 x + cos2 x = 1

ASYMPTOTY UKONE

y = mx + n

m

=

lim

x?

f

(x) x

,

n

=

lim

x?

[f (x)

-

mx]

POCHODNE

[f (x) + g(x)] = f (x) + g (x)

[f (x) - g(x)] = f (x) - g (x)

[cf (x)] = cf (x), gdzie c R

[f (x)g(x)] = f (x)g(x) + f (x)g (x)

f (x) g(x)

=

f

(x)g(x)-f (x)g g2(x)

(x) ,

o

ile

g(x)

=

0

[f (g(x))] = f (g(x))g (x)

[f (x)]g(x) = eg(x) ln f(x)

(c) = 0, gdzie c R

(xp) = pxp-1

( x)

=

1 2x

(

1 x

)

=

-

1 x2

(ax) = ax ln a

(ex) = ex

(loga x)

=

1 x ln a

(ln x)

=

1 x

(sin x) = cos x

(cos x) = - sin x

(tg x)

=

1 cos2 x

(ctg x)

=

-

1 sin2

x

(arc sin x)

=

1 1-x2

(arc cos x)

=

-

1 1-x2

(arc tg x)

=

1 1+x2

(arc ctg x)

=

-

1 1+x2

1

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