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Mathematics: Post your doubts here!

Zain Salman Dar

Zain Salman Dar

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Bumble_bee

Bumble_bee

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Assalamualikum and hello everyone.
I'm stuck in this question, so can anyone solve it for me?Would be of great help. Thanx.
The parametric equations of a curve are
x=2ɵ+cosɵ y=ɵ+sinɵ
where 0≤ɵ≤2π
1. Find dy/dx in terms of Ɵ.
2. Show that, at points on the curve where the gradient is 3/4, the parameter Ɵ satisfies an equation of the form
5sin(Ɵ+P)=2 , where the value of P is to be stated.
3. Solve the equation in part 2 to find the two possible values of Ɵ.
 
Bumble_bee

Bumble_bee

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Haider Ejaz said:
please help me in doing this question... thanks in advance :)View attachment 50852
Click to expand...
1) 2^x - 2^-x = 1 can be written as 2^x - 1/2^x = 1. And since y=2^x , the eqn can be written as y - 1/y = 1.
You can hence form the quad eqn y^2 - 1 = y (by multiplying both sides by y) which then rearranges to give y^2 - y -1=0.
2) You can solve the quad eqn involving y to give y= 1.618 and y= -0.618 (use quadratic formula to solve or the cal)
Now since y=2^x ,
1.618= 2^x. ln both sides to give ln 1.618 = x ln 2
x = ln 1.618/ ln 2 = 0.694 correct to 3 s.f .
y = -0.618 cannot be used to find a solution for x as ln negative values are undefined.

Hope you understood! You're welcome. :)
 
Haider Ejaz

Haider Ejaz

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Bumble_bee said:
1) 2^x - 2^-x = 1 can be written as 2^x - 1/2^x = 1. And since y=2^x , the eqn can be written as y - 1/y = 1.
You can hence form the quad eqn y^2 - 1 = y (by multiplying both sides by y) which then rearranges to give y^2 - y -1=0.
2) You can solve the quad eqn involving y to give y= 1.618 and y= -0.618 (use quadratic formula to solve or the cal)
Now since y=2^x ,
1.618= 2^x. ln both sides to give ln 1.618 = x ln 2
x = ln 1.618/ ln 2 = 0.694 correct to 3 s.f .
y = -0.618 cannot be used to find a solution for x as ln negative values are undefined.

Hope you understood! You're welcome. :)
Click to expand...
Great and Superb... Now i have understood it completely... Thank you very very much and may God bless you.
 
SitiPutri

SitiPutri

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Bumble_bee said:
Assalamualikum and hello everyone.
I'm stuck in this question, so can anyone solve it for me?Would be of great help. Thanx.
The parametric equations of a curve are
x=2ɵ+cosɵ y=ɵ+sinɵ
where 0≤ɵ≤2π
1. Find dy/dx in terms of Ɵ.
2. Show that, at points on the curve where the gradient is 3/4, the parameter Ɵ satisfies an equation of the form
5sin(Ɵ+P)=2 , where the value of P is to be stated.
3. Solve the equation in part 2 to find the two possible values of Ɵ.
Click to expand...

Answer attached.
 

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A

Abhay Ram

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Hi,
I am an A-Level Math student.
Can i get Math (P1,P3,M1,M2) chapter-wise past papers.
Thanks.

--Abhay
 
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