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Edexcel C4 Maths HELP

Hello,
If the gradient of curve is dy/dx = (-2/3)cot2t
Then how do I find the coordinates of the points where the tangent to the curve is parallel to the x-axis.
I've written the gradient as, (-2)/(3tan2t)
so surely if the tangent is parallel with the x axis, the numerator of this gradient must = 0?
Thanks
the equation of any line is y = mx + c

lines parallel to the x-axis have equations y = c which can be written in the form y = 0x + c.

therefore, since m = 0, dy/dx = 0. so dy = 0.
Reply 2
Avatar for Grewsters
Grewsters
OP
5
thank you! I understand that bit but isn't dy -2/3 or -2?
obviously -2/3 doesn't equate to 0 though so what is dy?
Reply 3
Avatar for Zacken
Zacken
22
Original post by Grewsters
Hello,
If the gradient of curve is dy/dx = (-2/3)cot2t
Then how do I find the coordinates of the points where the tangent to the curve is parallel to the x-axis.
I've written the gradient as, (-2)/(3tan2t)
so surely if the tangent is parallel with the x axis, the numerator of this gradient must = 0?
Thanks


Exactly, the numerator has to be 0, so -2 cot 2t = 0.

But cot 2t = cos 2t / sin 2t.

So -2 cos 2t = 0.

So cos 2t = 0.

Solve the equation cos x = 0 where x = 2t.
Reply 4
Avatar for B_9710
B_9710
18
If dy/dx=0 then cot2t=cos2t/sin2t=0
So cos2t=0.
Reply 5
Avatar for Grewsters
Grewsters
OP
5
Original post by Zacken
Exactly, the numerator has to be 0, so -2 cot 2t = 0.

But cot 2t = cos 2t / sin 2t.

So -2 cos 2t = 0.

So cos 2t = 0.

Solve the equation cos x = 0 where x = 2t.


ahhh yeah that makes sense now, thank you
Original post by Grewsters
Hello,
If the gradient of curve is dy/dx = (-2/3)cot2t
Then how do I find the coordinates of the points where the tangent to the curve is parallel to the x-axis.
I've written the gradient as, (-2)/(3tan2t)
so surely if the tangent is parallel with the x axis, the numerator of this gradient must = 0?
Thanks


Original post by Zacken
x


What past paper was this? I remember doing it quite a while back. :redface:
Original post by Zacken
Exactly, the numerator has to be 0, so -2 cot 2t = 0.

But cot 2t = cos 2t / sin 2t.

So -2 cos 2t = 0.

So cos 2t = 0.

Solve the equation cos x = 0 where x = 2t.


Yeah and if it says parallel to the y axis then dy/dx = o where the numerator is '0'
but the denominator is = 0 right?
Reply 8
Avatar for Zacken
Zacken
22
Original post by XxKingSniprxX
Yeah and if it says parallel to the y axis then dy/dx = o where the numerator is '0'
but the denominator is = 0 right?


What?
Original post by Zacken
What?


read op question. "how do I find the coordinates of the points where the tangent to the curve is parallel to the x-axis. "

I said if its parallel to the y axis the numerator is '0' and the denominator is = 0
right?

where in OP case you just treat dy/dx = 0 as normal.
Reply 10
Avatar for Zacken
Zacken
22
Original post by XxKingSniprxX
read op question. "how do I find the coordinates of the points where the tangent to the curve is parallel to the x-axis. "

I said if its parallel to the y axis the numerator is '0' and the denominator is = 0
right?

where in OP case you just treat dy/dx = 0 as normal.


tf you mean by 'the numerator is '0''?
Original post by Zacken
tf you mean by 'the numerator is '0''?


yeah so you would just set the denominator to zero
and solve if the question was asking for parallel to y axis.
Reply 12
Avatar for Zacken
Zacken
22
Original post by XxKingSniprxX
yeah so you would just set the denominator to zero
and solve if the question was asking for parallel to y axis.


yeah, that isn't what you were saying previously though
Reply 13
Avatar for Grewsters
Grewsters
OP
5
Original post by XxKingSniprxX
What past paper was this? I remember doing it quite a while back. :redface:


C3 Solomon C. I hate how there are no video walkthroughs for solomon papers so I come here for all my issues with them hahah

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