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Mathematics: Post your doubts here!

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Have a doubt in 2012 paper,
easy question , but dont seem to get it !
Question 5 (ii) .. ( 2 Marks )
For last question , how to draw Re z > 1 ? ( 1 Mark )
 

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mujhay dil ki nahi dimag ki awaaz chahye meri jaan.
Dude, first off, you really need to cool off and let go of that khuari a bit. Give the lady some respect. Secondly, what you are asking is pretty simple. Look, you need to find the angle between a curve and a tangent, right? That would require you to know two things: The gradient of the tangent to the curve and the other is the point on the curve to which you need angle from. Next you differentiate the equation of the curve and find the gradient of that point by substitution and now all you need to know is the fact that a gradient is just simple the ratio of the height of an point to the width of it, that means,

Rise/Run. Which is just like the tan formula, Tan@ = perp/base so if you take the tan inverse of the gradient of that point and then take the tan inverse of the gradient of the tangent, you will have two angles, subtract the larger angle from the smaller angle and you have the angle between a tangent and a point on the graph. Lastly, I would humbly ask you to remove that comment from the thread, it looks extremely degrading on such an intellectual forum.
 
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http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_11.pdf
Q5 pii , piii
How the heck do i find the range from domain, My freaking book sucks! ? :(
Generally how do you do it. I need help please.

I want part iii too, i am stuck at:
cos^2 (x)=0.6
How do you do after this or how do you calculate this thing:
x= cos^-2 (0.6)
haha, for the last part, you first take the square root on both the sides and then go on to take the inverse :D The rest of the questions, I will explain it to you in a separate post.
 
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http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_11.pdf
Q5 pii , piii
How the heck do i find the range from domain, My freaking book sucks! ? :(
Generally how do you do it. I need help please.

I want part iii too, i am stuck at:
cos^2 (x)=0.6
How do you do after this or how do you calculate this thing:
x= cos^-2 (0.6)
f(x) = 2 – 5(cosx)^2

maximum value of cosx = 1

since it is squared in the equation, cosx = -1 will give the same value for f(x) as cosx = 1

for max value of f(x), 5(cosx)^2 should be 0

therefore max f(x) = 2

for min value of f(x), cosx = 1 or cosx= -1

thus, minimum f(x) = -3
 
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