数学T paper 2讨论专区

恩媛

我有好多題math T的題目不會做...
有誰可以教我呢？？

Allmaths

我有好多題math T的題目不會做...
有誰可以教我呢？？
恩媛 发表于 1-4-2012 03:10 PM

你不post题目上来就肯定没有人可以帮到你

peaceboy

回复 682# 恩媛


    学校里面有一个叫老师的生物会教你的

恩媛

1 ）use the substitution t = tan (theta) to express √(1-sin 2theta /1+sin2theta) in terms of tan (theta)
2) use substitution t = tan (theta)/2
prove : sec (theta) + tan  (theta) =tan (  theta/2 + 1/4π )

恩媛

回复 684# peaceboy

我們的老師正在放產假....

whyyie

1 ）use the substitution t = tan (theta) to express √(1-sin 2theta /1+sin2theta) in terms of tan (theta)
恩媛 发表于 2-4-2012 05:07 PM

tan (theta) = t
sin (theta) = t / √(1+t^2)
cos(theta) = 1 / √(1+t^2)

√(1-sin 2theta /1+sin2theta)
= √((1 - 2 sin(theta) cos (theta)) / (1+2sin(theta)cos(theta)))
= (t - 1) / (t + 1)
= (tan(theta) - 1) / (tan(theta)+1)

死亡芭比

Solve the differential equation  dy/dy= xy/x^2+ y^2. Find the particular solution if y=1 and x=3. 请问有谁可以帮帮我啊？？

Allmaths

Solve the differential equation  dy/dy= xy/x^2+ y^2. Find the particular solution if y=1 and x=3. 请 ...
死亡芭比 发表于 14-4-2012 06:59 PM

   dy/dx=(xy)/(x^2+y^2)
  let y=vx
dy/dx=v+x(dv/dx)

v+x(dv/dx)=(vx^2)/(x^2+v^2x^2)
v+x(dv/dx)=v/(1+v^2)
v-[v/(1+v^2)]=-x(dv/dx)
v^3/(1+v^2)=-x(dv/dx)
-∫ (1/x) dx=
∫[(1+v^2)/v^3] dv
-ln x + A=
∫[(1/v^3)+(1/v)]dv
-ln x + A= -1/(2v^2)+ln v + B
-ln x + A=-[x^2/(2y^2)]+ln(y/x) + B
-ln x + A=-[x^2/(2y^2)]+ln y-ln x + B
ln y=[x^2/(2y^2)]+A-B
ln y=[x^2/(2y^2)]+C                            (C=A-B)

死亡芭比

请问怎样differentiate (ln cot x)?

peaceboy

回复 690# 死亡芭比


    let cot x = u
du/dx = - cosec^2 x

y = ln u
dy/du = 1/u

du/dx = dy/du * du/dx
         = - cosec^2 x / cot x
        = - 1/sin^2 x * tan x
        = - 1/sin^2 x * (sin x / cos x)
       = - 1/ sin x cos x
       = - 2/2sin x cos x
       = -2 / sin 2x



** shorter way formula : d[ ln f(x) ] /dx = f '(x) / f(x)

jose

Find the range of values of θ between 0 and 2π such that sin 2θ > sin  θ
[graphical methods are accepted, but any numerical value must be calculated.]

Allmaths

Find the range of values of θ between 0 and 2π such that sin 2θ > sin  θ
[graphical methods ar ...
jose 发表于 30-6-2012 03:42 PM

    sin 2θ > sin θ
2sin θ cos θ > sin θ
2sin θ cos θ -sin θ > 0
(sin θ)(2cos θ -1) > 0
sin θ > 0                            or                                cos θ > 1/2
0<θ<pi                                                            0<θ<pi/3   or   5pi/3<θ<2pi




sin θ < 0                            or                                cos θ <1/2
pi<θ<2pi                                                              pi/3<θ<5pi/3


find intersections between all the range,


Answer: {θ: 0<θ<pi/3   or    pi<θ<5pi/3}

booboo

prove given trigonometric identities...
cos&#8289;4z≡8&#8289;〖〖cos〗^4 z〗-8〖cos〗^2 z+1≡〖8cos〗^4 z-〖8sin〗^2 z+1

menglee90

booboo 发表于 28-7-2012 08:46 PM
prove given trigonometric identities...
cos&#8289;4z≡8&#8289;〖〖cos〗^4 z〗-8〖cos〗^2 z+1≡ ...

cos 4z
= 2 cos^2 2z - 1
= 2 [2 cos^2 z -1]^2 - 1
= 2 [4 cos^4 z - 4 cos^2 z + 1] - 1
= 8 cos^4 z - 8 cos^2 z + 1

后面那个不懂你type什么，帮不到你

booboo

menglee90 发表于 28-7-2012 10:59 PM
cos 4z
= 2 cos^2 2z - 1
= 2 [2 cos^2 z -1]^2 - 1

哇，太厉害啦！ 非常感谢！

cos&#8289;4z≡8&#8289;cos^4 z -8cos^2 z ≡ 8sin^4 z- 8sin^2 z +1

原来我之前把后面的type错了...
对不起呀！

menglee90

booboo 发表于 30-7-2012 06:47 PM
哇，太厉害啦！ 非常感谢！

cos&#8289;4z≡8&#8289;cos^4 z -8cos^2 z ≡ 8sin^4 z- 8sin^ ...

8sin^4 z- 8sin^2 z +1有问题？
8&#8289;cos^4 z -8cos^2 z + 1 不可能等于 8sin^4 z- 8sin^2 z +1

booboo

menglee90 发表于 30-7-2012 07:15 PM
8sin^4 z- 8sin^2 z +1有问题？
8&#8289;cos^4 z -8cos^2 z + 1 不可能等于 8sin^4 z- 8sin ...

不是，我之前把8sin^4 z- 8sin^2 z +1type成〖8cos〗^4 z-〖8sin〗^2 z+1
题目会不会是prove cos&#8289;4z≡8sin^4 z- 8sin^2 z +1？？


#我solve到了！！

永遠愛著許瑋倫

A boat is travelling at speed of 30 knots.A yacht is sailing northwards at a speed of 10 knots.At 1300 hours,the boat is 14 nautical miles to the north-easy of the yacht.
(a)Find the direction in which the boat should be travelling in order to intercept the yacht
(b)At what time the intersection occur?

哪個大大可以指教?!!

genji

prove that :

sin2x(cos4x+cos8x+12x)=cos8x sin6x

我被那个12x打败了，请高手帮忙

还有什么

genji 发表于 2-10-2012 09:24 PM
prove that :

sin2x(cos4x+cos8x+12x)=cos8x sin6x

很难啊。在哪儿找来的题目啊？我做了很久也做不到。

请问你其他的都做到吗除了12x ?