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Cambridge Prelim MX1 Textbook Marathon/Q&A (2 Viewers)

kawaiipotato

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

^
Could have also used the idenity
Tan (90+x) = tan (90-(-x))= cot (-x) = -cotx
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So the question says Find the acute angle and the obtuse angle between the lines:

2x - y + 1 = 0 and 11x - ( 8 + 5squaroot3)y + 5sqrt3 = 0

So I get Thetha = 30 and that is obviously the acute angle

Now finding the obtuse angle, is it as simple as saying 180 - 30 , so 150

The answer is 30, and 150

or is there more working necessary for obtuse angle find ??
 

si2136

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So the question says Find the acute angle and the obtuse angle between the lines:

2x - y + 1 = 0 and 11x - ( 8 + 5squaroot3)y + 5sqrt3 = 0

So I get Thetha = 30 and that is obviously the acute angle

Now finding the obtuse angle, is it as simple as saying 180 - 30 , so 150

The answer is 30, and 150

or is there more working necessary for obtuse angle find ??
That's it. But did you use the formula to find out the acute/obtuse angle?
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

what is lim E -> 0 of E^2 / cos^2 E

The answer says 0.

Why is that?? And not 1 ??
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Find dy/dx in terms of x and y by differentiating implicitly:

sin x + cos y = 1
 

kawaiipotato

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Differentiating with respect to x means differentiating another variable will give the change in variable with respect to x
So differentiating a y will give dy/dx
sinx + cosy = 1
Diff. Wrt x
d(sinx)/dx + d(cosy)/dx = d(1)/dx
==> cosx - siny * (dy/dx) = 0
dy/dx = cosx/siny
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Given the parametric equations x = e^t cost , y = e^t sint, show that dy/dx = tan ( t + pi/4 ) .
 

kawaiipotato

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Note that y/x = tanx
Aim: show dy/dx = tan (pi/4 + t)
Note the tan expansion: tan (a+b) = (tana + tanb)/(1-tanatanb)
Hence tan (pi/4 + t) = (1 + tant)/(1-tant)
So now your aim is to show:
dy/dx = (1+ y/x)/(1-y/x) = (x+y)/(x-y)

dy/dx = dy/dt * dt/dx
dy/dt = e^t sint + e^t cost (product rule )
dx/dt = e^t cost - e^t sint (product rule)

So dy/dx = (e^t sint + e^t cost)/(e^t cost - e^t sint)
= (x+y)/(x-y) as required
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Use the expansion of cos(A+ B) and cos(A-B) to prove that

cosS - cosT = -2sin1/2 (S + T)sin1/2 (S -T)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

How do you find the derivative of

y = log base e ( cosx)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

what is the derivative of cos^5 3x .
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So we know x degree is xpi/180 rad

Hence find:

Derivative of (tan (x degrees + 45 degrees))
 

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