Mathematics: Post your doubts here!

[Konstantino Nikolas]

acosθ + bsinθ = rsin(θ+α) or rsin(θ-α) or rcos(θ+α) or rcos(θ-α)

How do I know when to use what? :O

 

[nehaoscar]

acosθ + bsinθ = rsin(θ+α) or rsin(θ-α) or rcos(θ+α) or rcos(θ-α)

How do I know when to use what? :O

Learn them:
acosθ + bsinθ = rcos(θ-α)
acosθ - bsinθ = rcos(θ+α)
asinθ + bcosθ = rsin(θ+α)
asinθ - bcosθ = rsin(θ-α)
When cos is first it's rcos and the signs in brackets are opposite to LHS
When sin is first it's rsin and the signs in brackets are same as LHS

 

[Konstantino Nikolas]

Learn them:
acosθ + bsinθ = rcos(θ-α)
acosθ - bsinθ = rcos(θ+α)
asinθ + bcosθ = rsin(θ+α)
asinθ - bcosθ = rsin(θ-α)
When cos is first it's rcos and the signs in brackets are opposite to LHS
When sin is first it's rsin and the signs in brackets are same as LHS

I didn't know this ... damn, tysm!!!

 

[nehaoscar]

I didn't know this ... damn, tysm!!!

Welcome

 

[Konstantino Nikolas]

Find all values of x between 0 and degrees for which cosx - 2sinx = 1 .

Given Ans: 0
My Ans: 36.9

How are they getting 0? :/

 

[Devinky]

acosθ + bsinθ = rsin(θ+α) or rsin(θ-α) or rcos(θ+α) or rcos(θ-α)

How do I know when to use what? :O

It has to be given. Otherwise anything works because sin x = cos (90-x).

 

[Konstantino Nikolas]

It has to be given. Otherwise anything works because sin x = cos (90-x).

anything works but it is simplest using a particular method ... you know, time management and all

 

[holoholo]

Can someone please explain how to get a second vector for the question (ii) for the vector product ?

 

[Devinky]

Can someone please explain how to get a second vector for the question (ii) for the vector product ?

View attachment 59259

You need two vectors that lie in the plane. Then cross both of them to find the normal vector.
The first vector is i + 2j + k (the direction vector of l)
The second vector is (4i-2j+2k)-(2i+2j+k), since both points are in the plane the vector between them is in the plane.
Note: cross-product is NOT required for Maths P3 (only required for F. Maths). You only need to find a vector that is perpendicular to both of them and this is one of the techniques.

 

[Konstantino Nikolas]

Could anyone please help out with the second part?
ms:

 

[The Sarcastic Retard]

View attachment 59269
Could anyone please help out with the second part?
ms:
View attachment 59270

Use binomeal expansion.

 

[Konstantino Nikolas]

Use binomeal expansion.

lol i know that ... i didn't get the right answer

 

[nehaoscar]

View attachment 59269
Could anyone please help out with the second part?
ms:
View attachment 59270

So first part you have 3/3-2x + -x-2/x^2+4
For binomial expansion as mentioned in data booklet we need the bracket like (1+x)^n
So change 3/3-2x ==> 3/3(1-(2x/3)) ==> (1-(2x/3))^-1

• 1) And expand (1-(2x/3))^-1

Similarly
-x-2/x^2+4 ==> -x-2/4((x^2/4)+1) ==> 4^-1(-x-2)((x^2/4)+1)^-1

• 2) Expand ((x^2/4)+1)^-1 and then multiply the expansion by 4^-1(-x-2)

Now add 1 and 2 to obtain full expansion of 3/3-2x + -x-2/x^2+4

 

[Konstantino Nikolas]

So first part you have 3/3-2x + -x-2/x^2+4
For binomial expansion as mentioned in data booklet we need the bracket like (1+x)^n
So change 3/3-2x ==> 3/3(1-(2x/3)) ==> (1-(2x/3))^-1

• 1) And expand (1-(2x/3))^-1

Similarly
-x-2/x^2+4 ==> -x-2/4((x^2/4)+1) ==> 4^-1(-x-2)((x^2/4)+1)^-1

• 2) Expand ((x^2/4)+1)^-1 and then multiply the expansion by 4^-1(-x-2)

Now add 1 and 2 to obtain full expansion of 3/3-2x + -x-2/x^2+4

Ohh such a stupid mistake i made ... I'm soo sorry for making you do it Thank you! I realised my mistake ... instead of substituting value of A, i had substituted value of B ... I can only pray to God I don't make such mistakes in my exam.
Thank you.

 

[nehaoscar]

Ohh such a stupid mistake i made ... I'm soo sorry for making you do it Thank you! I realised my mistake ... instead of substituting value of A, i had substituted value of B ... I can only pray to God I don't make such mistakes in my exam.
Thank you.

Hahaha no problem!

 

[staying alive]

Re: Maths help available here!!! Stuck somewhere?? Ask here!
Could you help me with a solution to the Chapter 11 review problems in new syllabus mathematics 3 by lee peng yee?
UPDATE: Link to Sequences Help by destined007 added!

 

[Educationist]

Does anyone have
Prof. Dr. Nabeel R. Elias' notes for AL 9709 ?

 

[Copy Cat]

(ii) & (iii) part

 

[Konstantino Nikolas]

View attachment 59296
(ii) & (iii) part

 

[staying alive]

Could anyone help me with these problems?Would be greatly appreciated