O-Level Additional Math

[iFruit]

SKT:

Hi iFruit,


Refer to the original question, x/4 is at the first quadrant, why -2sin x/4 is valid?

TIA

Hi SKT,

In the original question, [2 + √(2 + 2 cos x)] is a +ve number because cos x is +ve.

we need to find the square root of √(a +ve number), which will have a +ve and a -ve root.

Sure, x/4 is in the first quadrant but that is not related to the value of √[2 + √(2 + 2 cos x)] at all. The sign of cos x/2 matters only when taking the square root of √(4cos² x/2), because we need to keep (2 + √(4cos² x/2)) > 2, so we must choose -ve root.

Just for argument's sake, let's say x=300, then [2 + √(2 + 2 cos 300 )] = 2 + √3 =3.732

so √3.732 = ±1.93

Hope this helps.

[Muffins]

woah..... these questions making my head spin already :faint: :faint:

[iFruit]

Muffins:

woah..... these questions making my head spin already :faint: :faint:

Welcome to the real world mate ! We have no Mohammads and Alis exchanging marbles or silly old mothers trying to pick up their daughters from the schools at constant speed every day here.

We just have beautiful x's and y's and before you blink sin As, cos Bs and Sec Cs.

[SKT]

Hi,


Find the equations of the tangents from (2, -3) to the curve y = x + x².

TIA

[iFruit]

SKT:

Hi,


Find the equations of the tangents from (2, -3) to the curve y = x + x².

TIA

let's say the point at which the line and curve meet is (x, y) = (x, x+x²).

Then, Slope of tangent = (x+x²+3)/(x-2)

but slope of tangent = dy/dx of curve = d( x + x² )/dx = 1+2x

so (x+x²+3)/(x-2) = 1+2x--> x+x²+3 = 2x² -3x -2-->x²-4x-5 = 0 -> (x+1)(x-5) = 0---> x = -1 or 5

when x =-1, y = x + x² = 0, m = 1+2x = -1
when x = 5, y = 30, m = 11

The lines of the equation

y = -x + C1, y = 11x +C2,

Solving for point ( 2,-3), we get the tangents of curves

y = -x-1,

y = 11x -25


HTH

[SKT]

Hi,


A man 1.5 m tall is walking at a speed of 2 m/s away from a lamppost which has a lamp 5 m above the ground. Find the speed of the top of his shadow.

TIA

[iFruit]

SKT:

Hi,


A man 1.5 m tall is walking at a speed of 2 m/s away from a lamppost which has a lamp 5 m above the ground. Find the speed of the top of his shadow.

TIA

distance of man from lamp post at time t = 2t
Let distance of top of shadow from lamp post = s

tan x = 5/s = 1.5/(s-2t)--->5s -10t = 1.5s

3.5s = 10t

ds/dt = 10/3.5 = 20/7 m/s

[mramk]

Guan Hui:

Hi parents, just wondering why is there not a thread for secondary school maths questions and decided to start on one.(inspired by mathsguru contribution to this community)


So... yup this is for Q&A for secondary school maths questions.

Please state the level of the question when posting the question for the convenience of knowing which method should be used to explain the answers.(e.g. Sec 1)

Hope it helps!

Hi Guan Hui, thanks for your service. Could you please help with below question:

prove the identity: cos(x).cot(x) + sin(x) = cosec(x). (O level A-Math)

Thank alot.

[wmd]

mramk:

prove the identity: cos(x).cot(x) + sin(x) = cosec(x). (O level A-Math)

Thank alot.

cos(x).cot(x) + sin(x)
=cos(x)*(cos(x)/sin(x))+sin(x)
=(cos(x))^2/sin(x) + sin(x)
=((cos(x))^2+(sin(x))^2)/sin(x)
=1/sin(x)
=cosec(x)

[YLH88]

Hi achemtutor,


Thank you!