Introduktion till matematikstudier

Question 1

pq-formeln

X^2+px+q=0

Answer 1

x=−(p/2)(+/−)√((p/2)^2-q)

Question 2

a^x•a^y

Answer 2

a^x+y

Question 3

(a^x)^y

Answer 3

a^xy

Question 4

Y=10^x

Answer 4

X=lg(y)

Question 5

y=e^x

Answer 5

x=ln(y)

Question 6

lg(x)+lg(y)

Answer 6

lg(xy)

Question 7

lg(x)-lg(y)

Answer 7

lg(x/y)

Question 8

lg(x^p)

Answer 8

p•lg(x)

Question 9

Cirkel area

Answer 9

A= πr^2= (πd^2)/4

Question 10

Cirkel omkrets

Answer 10

O=2 πr= πd

Question 11

Trigonometri
sin(v)
cos(v)
tan(v)

Answer 11

sin(v)=motstående/hypotenusan
cos(v)=närliggande/hypotenusan
tan(v)=motstående/närliggande=sin(v)/cos(v)

Question 12

Enhetscirkeln
sin(v)
cos(v)
tan(v)

Answer 12

sin(v)=y
cos(v)=x
tan(v)=y/x

Question 13

Trigonometriska ettan

Answer 13

sin^2(v)+cos^2(v)=1

Question 14

sin(v+w)

Answer 14

sin(v+w)=sin(v)cos(w)+cos(v)sin(w)

Question 15

sin(v-w)

Answer 15

sin(v-w)=sin(v)cos(w)-cos(v)sin(v)

Question 16

cos(v+w)

Answer 16

cos(v+w)=cos(v)cos(w)-sin(v)sin(w)

Question 17

cos(v-w)

Answer 17

cos(v-w)=cos(v)cos(w)+sin(v)sin(u)

Question 18

sin(2v)

Answer 18

sin(2v)=2sin(v)cos(v)

Question 19

cos(2v)

Answer 19

cos(2v)=cos^2(v)-sin^2(v)
cos(2v)=2cos^2(v)-1
cos(2v)=1-2sin^2(v)

Question 20

|z|

Answer 20

|z|=r= √((x^2)+(y^2))

Question 21

de Moivres formel

Answer 21

z^n=(r(cos(v)+i•sin(v))^n=(r^n)•(cos(nv)+isin(nv))

Question 22

Summaformel för aritmetiska summor

Answer 22

n(a1 + an)/2

Question 23

Summaformel för geometriska summor

Answer 23

r≠1 → a(1-r ^n)(1-r)

r=1 → na