Equations

Question 1

Standard equation of a circle

Answer 1

(x - h)^2 + (y - k)^2 = a^2

Question 2

An even function

Answer 2

f(-x) = f(x)

Question 3

An odd function

Answer 3

f(-x) = -f(x)

Question 4

The Quadratic Formula

Answer 4

(-b±√(b²-4ac)) / (2a)

Question 5

π radians

Answer 5

180 degrees

Question 6

The circumference of a circle

Answer 6

2πr

Question 7

(a + b)^2 =

Answer 7

a^2 + 2ab + b^2

Question 8

(a - b)^2 =

Answer 8

a^2 - 2ab + b^2

Question 9

(a + b)(a - b) =

Answer 9

a^2 - b^2

Question 10

sin x =

Answer 10

opposite / hypotenuse (SOH)

Question 11

cos x =

Answer 11

adjacent / hypotenuse (CAH)

Question 12

tangent x =

Answer 12

opposite / adjacent (TOA)

Question 13

Omregningsformelen

Answer 13

n / 180 = v / π

Question 14

Sinusfunksjon

Answer 14

f(x) = a*sin(kx + c) + d

Question 15

Likning for likevekstlinjen i en sinusfunksjon

Answer 15

d, y = (maksverdi + minimumsverdi) / 2

Question 16

Amplituden i en sinusfunksjon

Answer 16

a = |a| = maksverdi - likevekstlinjen

Question 17

Likning til en periode i en sinusfunksjon

Answer 17

p * k = 2π
eller
p = 2π / k

Question 18

Når skjærer sinusfunksjonen likevekstlinja?

Answer 18

kx + c = 0

Question 19

Asymptoter til tangens

Answer 19

kx = π / 2 + n * π

Question 20

Nullpunkt til tangens

Answer 20

kx = n * π

Question 21

(sinx)’

Answer 21

cosx

Question 22

(cosx)’

Answer 22

-sinx

Question 23

(tanx)’

Answer 23

1 / cos^2x eller 1 + tan^2x

Question 24

Enhetsformel

Answer 24

cos^2x + sin^2x = 1

Question 25

Ettpunktsformelen

Answer 25

y - y1 = a(x - x1)

Question 26

Faseforskyvning

Answer 26

-k * x0 (x0 = x-verdi til 1. toppunkt)

Question 27

Aritmetisk tallfølge

Answer 27

an = a1 + (n-1)d

Question 28

Sum av aritmetisk rekke

Answer 28

Sn = ((a1 + an)n) / 2

Question 29

∫x^ndx =

Answer 29

1 / (n + 1) * x^n+1 + C

Question 30

Konvergent geometrisk rekke

Answer 30

S = a1 / (1 - k) ,når |k| <1

Question 31

Kvotient til en geometrisk følge

Answer 31

(ai + 1) / ai = k

Question 32

an til geometrisk rekke

Answer 32

a1 * k^n-1

Question 33

Sn til geometrisk rekke

Answer 33

a1* (k^n - 1) / (k - 1)

Question 34

Konvergent geometrisk rekke

Answer 34

S = a1 / (1 - k)

Question 35

Komplekse tall: z = ? og |z| = ?

Answer 35

z = a + bi

Question 36

Komplekse tall: i = ?

Answer 36

i = sqrt-1

Question 37

Trigonometrisk / polar form av z

Answer 37

|z| (cosθ + isinθ)

Question 38

Eulers formel

Answer 38

e^iθ = cosθ + isinθ

Question 39

(f^-1)'(x)

Answer 39

1 / f'(f^-1(x))

Question 40

Hvis: y' = k * y

Answer 40

y(t) = Ce^kt

Question 41

cosh(x) =

Answer 41

(e^x + e^-x) / 2

Question 42

sinh(x) =

Answer 42

(e^x - e^-x) / 2

Question 43

cosh^2(x) - sinh^2(x) =

Answer 43

1

Question 44

(cosh(x))' =

Answer 44

sinh(x)

Question 45

(sinh(x))' =

Answer 45

cosh(x)

Question 46

ay'' + by' + cy = 0

Answer 46

Karakteristisk likning: ar^2 + br + c = 0