Kursprov Matte 4

Question 1

v till rad

Answer 1

180v/pi

Question 2

rad till v

Answer 2

pi*v / 180

Question 3

Motsatta vinklar

Answer 3

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

Question 4

Komplementvinklar

Answer 4

sin(90-v) = cos v
cos(90-v) = sin v

Question 5

sin(u+v)

Answer 5

sin(u) * cos(v) + cos(u) * sin (v)

Question 6

sin(u-v)

Answer 6

sin(u) * cos(v) - cos(u) * sin(v)

Question 7

cos(u+v)

Answer 7

cos(u)cos(v) - sin(u)sin(v)

Question 8

cos(u-v)

Answer 8

cos(u)cos(v) + sin(u)sin(v)

Question 9

sin 2v

Answer 9

2 sin v cos v

Question 10

cos 2v

Answer 10

cos^2 v - sin^2 v

Question 11

Egenskaper för y = A sin(Bx + C) + D

Answer 11

Amplitud: A
Förskjutning X-led: C
Period: 360/B
Förskjutning Y-led: D

Question 12

Beskriv y = a sin x + b cos x

med en sinuskurva

Answer 12

y = sqrt(a^2 + b^2) sin(x + tan^-1(b/a)

Question 13

Vinkelhastighet samt tiden för en period för

f(t) = sin vt

Answer 13

v = 2pi / t
T = 2pi/v

Question 14

Derivera
sin x
cos x
tan x

Answer 14

cos x
-sin x
1/(cos^2 x)

Question 15

Derivera a^x

Answer 15

ln a * a^x

Question 16

Derivera ln x

Answer 16

1/x

Question 17

Derivera a(x)*b(x)

Answer 17

a’(x)*b(x) + a(x) * b’(x)

Question 18

Derivera a(x)/b(x)

Answer 18

( a’(x) * b(x) - a(x) * b’(x) ) / (b(x))^2

Question 19

Gör primitiv funktion av:
x^n
1/x
sin kx
cos kx

Answer 19

(x^n+1)/(n+1) + C
ln x + C
- (cos kx )/ k + C
(sin kx)/k + C

Question 20

Eulers formel

Answer 20

re^(iv) = r(cos v + i sin v)

Question 21

Eulers identitet

Answer 21

e^(ipi) = -1