Forumet - Matte D - trigonometriproblem

Matte D - trigonometriproblem

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Rand0mGuy:


cos(2v-π/3) = cos(v)
-π ≤ v ≤ π
p heltal

cos(2v-π/3) = cos(v)
[ {cos(a) = cos(-a), cos(a) = cos(a+p*2π)} →
(cos(a) = cos(b) → {a = -b+p*2π, a = b+p*2π}) ]
{2v-π/3 = -v+p*2π, 2v-π/3 = v+p*2π}

2v-π/3 = -v+p*2π
2v+v = π/3+p*2π
3v = π/3+p*2π
3v/3 = (π/3+p*2π)/3
v = π/(3*3)+p*2π/3
v = π/3²+p*2π/3
v = π/9+p*2π/3

2v-π/3 = v+p*2π
2v-v = π/3+p*2π
v = π/3+p*2π

{v = π/9+p*2π/3, v = π/3+p*2π}

v = π/9+p*2π/3
-π ≤ v ≤ π
-π ≤ π/9+p*2π/3 ≤ π
-π/π ≤ (π/9+p*2π/3)/π ≤ π/π
-1 ≤ π/(9π)+p*2π/(3π) ≤ 1
-1 ≤ 1/9+(2/3)p ≤ 1
-1-1/9 ≤ (2/3)p ≤ 1-1/9
-9/9-1/9 ≤ (2/3)p ≤ 9/9-1/9
-(9+1)/9 ≤ (2/3)p ≤ (9-1)/9
-10/9 ≤ (2/3)p ≤ 8/9
3(-10/9) ≤ 3(2/3)p ≤ 3*8/9
-10/3 ≤ 2p ≤ 8/3
-10/(3*2) ≤ 2p/2 ≤ 8/(3*2)
-10/6 ≤ p ≤ 8/6
-5/3 ≤ p ≤ 4/3

-5/3 ≤ p ≤ 4/3
p heltal
-2 < -5/3 < -1
1 < 4/3 < 2
-1 ≤ p ≤ 1

p = -1
v = π/9-1*2π/3
v = π/9-2π/3
v = (1/9-2/3)π
v = (1/9-6/9)π
v = ((1-6)/9)π
v = (-5/9)π
v = -(5/9)π

p = 0
v = π/9+0*2π/3
v = π/9

p = 1
v = π/9+1*2π/3
v = π/9+2π/3
v = (1/9+2/3)π
v = (1/9+6/9)π
v = ((1+6)/9)π
v = (7/9)π

v = π/3+p*2π
-π ≤ v ≤ π
-π ≤ π/3+p*2π ≤ π
-π/π ≤ (π/3+p*2π)/π ≤ π/π
-1 ≤ π/(3π)+p*2π/π ≤ 1
-1 ≤ 1/3+p*2 ≤ 1
-1-1/3 ≤ 2p ≤ 1-1/3
-3/3-1/3 ≤ 2p ≤ 3/3-1/3
-(3+1)/3 ≤ 2p ≤ (3-1)/3
-4/3 ≤ 2p ≤ 2/3
-4/(3*2) ≤ 2p/2 ≤ 2/(3*2)
-4/6 ≤ p ≤ 2/6
-2/3 ≤ p ≤ 1/3

-2/3 ≤ p ≤ 1/3
p heltal
-1 < -2/3 < 0
0 < 1/3 < 1
p = 0

p = 0
v = π/3+0*2π
v = π/3

v = -(5/9)π
v = π/9
v = π/3
v = (7/9)π

v Є {-(5/9)π, π/9, π/3, (7/9)π}
det här e skit enkelt. kollA
cos(2v-π/3)= cos v
cos 2v-cos π/3= cos v....................... multiplicerar
cos 2v-1/2= cos v .................... eftersom cos π/3 e 1/2
cos 2v-cos v-1/2= 0
cos v-1/2=0
cos v = 1/2
v=cos-1(1/2)
v=π/3
nu ska vi kolla intervallet. -π till +π: och eftersom det e cos används det här formulet
x=±v +N2π.......N e antal varv i unit cirkel
=± π/3 + N2π......nu ska vi se till att svaret ligger i intervallet.asså -π till +π
då blir x = -2π/3 , -π/3 ,0 , π/3 , 2π/3
jag e en geni[cool]

Spana också in:

valentinos:

fråga din matte lärare. det var det bästa svaret du nånsin kommer få!!


Min klass är ganska dum, plus att vi har en så kallad hjälplista på tavlan där man ska skriva upp sig. På grund av klassens dumhet, så uppgår listan mot en sådär 15-20 namn inom 5 minuter efter lektionens start.

Så det är inget alternativ :(