Hi, I absolutely love this channel! You're my SAVIOUR, so I have subscribed already. Would you mind doing a video on geometric sequences, preferably before the GCSE 2024 maths exam? I know there is a lot of hard work behind that but really need that. Would be highly appreciated!
because 5 is the distance from the origin - so even tho the coordinate is -5 (just meaning 5 less than the origin) the distance between the 2 points is till just 5
12:09 this might be a dumb question but how would we use trigonometry to find out A and B and in what cases would it be a preferable method to just finding the equation of the tangent.
Never a stupid question. I will do my best to explain. If you draw in the line OP and then a vertical line down from P to the x-axis and call the point where this vertical hits the x-axis say Q. Triangle OPQ is a right angled triangle as angle OQP is 90° Since P = (12, 18) OQ = 12 and QP = 18 You can then use these two sides to find angle POQ using trigonometry (inverse tan of 18/12) and also OP using Pythagoras (square root of 18^2 + 12^2). If you now rub out line PQ and look at triangle OPB. This triangle is also right angled since angle OPB = 90°. This is because of circle theorems and a radius meets a tangent at 90°. You can use the angle you found along with the side OP to find the side length of OB using trigonometry again. Once you have the length of OB you must know what B's coordinates are since it will be the length of OB for the x-coordinate and the y-coordinate will be 0. The same idea with point A just the other way. As you can see it is a bit lengthly but only requires knowledge of right angled triangles. Technically the skills used are lower level however spotting how to use them is tricky and lengthly. It wouldn't matter which one you used but since the video is about equation of tangents I chose to just do that but often some smart people like to comment things like "btw you could have done it like this" (as if I am unaware) so I just pre-empt them. Hope that helps and once again, there is never a stupid question, always ask and quite possibly lots of other people were thinking the same thing.
Thank you so much for the quick reply, I was trying to answer the question using trigonometry after asking the question and ended up with essentially the same method (stopped after solving point b) you gave which was a relief. I do agree that this method is lengthier than using the tangent of the circle but it makes sense why you mention it in the video so thank you for the clarification. Recently found out about your videos and website, will be recommending to my friends as they are all exceptional resources👍
Hi there , today I did my higher exam paper 1 and one of the questions were to write down the equation of a parabolla can you make a video related to parabolla 😊
With content like this, can't wait for your platform to come out!
8:40 why did the co ordinate k turn to -k when the y coordinate is still in the positive area??😢
We are finding the gradient of the radius by doing change in y over change in x.
The y value has gone from k to 0 so a change of -k
Hi, I absolutely love this channel! You're my SAVIOUR, so I have subscribed already. Would you mind doing a video on geometric sequences, preferably before the GCSE 2024 maths exam? I know there is a lot of hard work behind that but really need that. Would be highly appreciated!
I will try!
Yes pls lots of hard questions on geometric sequences @@1stClassMaths
I’m confused why at 8:47 the points are (-5,k), but the labels are +5 and -k. Why have they been switched??
me too
because 5 is the distance from the origin - so even tho the coordinate is -5 (just meaning 5 less than the origin) the distance between the 2 points is till just 5
oh it might be easier just to explain that u cant have a negative length so the base of the triangle cant be -5 long
12:09 this might be a dumb question but how would we use trigonometry to find out A and B and in what cases would it be a preferable method to just finding the equation of the tangent.
Never a stupid question. I will do my best to explain.
If you draw in the line OP and then a vertical line down from P to the x-axis and call the point where this vertical hits the x-axis say Q.
Triangle OPQ is a right angled triangle as angle OQP is 90°
Since P = (12, 18)
OQ = 12 and QP = 18
You can then use these two sides to find angle POQ using trigonometry (inverse tan of 18/12) and also OP using Pythagoras (square root of 18^2 + 12^2).
If you now rub out line PQ and look at triangle OPB. This triangle is also right angled since angle OPB = 90°. This is because of circle theorems and a radius meets a tangent at 90°.
You can use the angle you found along with the side OP to find the side length of OB using trigonometry again. Once you have the length of OB you must know what B's coordinates are since it will be the length of OB for the x-coordinate and the y-coordinate will be 0.
The same idea with point A just the other way.
As you can see it is a bit lengthly but only requires knowledge of right angled triangles. Technically the skills used are lower level however spotting how to use them is tricky and lengthly. It wouldn't matter which one you used but since the video is about equation of tangents I chose to just do that but often some smart people like to comment things like "btw you could have done it like this" (as if I am unaware) so I just pre-empt them.
Hope that helps and once again, there is never a stupid question, always ask and quite possibly lots of other people were thinking the same thing.
Thank you so much for the quick reply, I was trying to answer the question using trigonometry after asking the question and ended up with essentially the same method (stopped after solving point b) you gave which was a relief. I do agree that this method is lengthier than using the tangent of the circle but it makes sense why you mention it in the video so thank you for the clarification. Recently found out about your videos and website, will be recommending to my friends as they are all exceptional resources👍
phenomenal teaching thanks so much :)
You're very welcome!
Thanks so much for making these videos. Just a heads up, I found that the link didn't work for this video on the first class maths website.
Thanks for letting me know. I will fix it now.
At 9.43 when we find k= 6 and it is -k=-6 why have we turned it to a negative k please 🙂
For the gradient we do change in y/change in x
Since the slope is downwards the change will be negative k so that we get a negative gradient.
Isn’t example 1 with a downward slope?
@@boipelomolepo I am referring to the gradient of the radius rather than the tangent.
Ohk thank you sir
How would you find where it crosses the X axis?
y is 0
Can you make a triple science account too
Thank you so much
You're most welcome
Thanks,really helpfull,hooe u will do A level maths,as we will finish our gces soon😭
I will try my best
Hi there , today I did my higher exam paper 1 and one of the questions were to write down the equation of a parabolla
can you make a video related to parabolla 😊
The equation of a parabola is a quadratic. It's in the form an² + bn + c. I'm not sure if this helps.
thank u so much sir💗
i love these questions
thank you sm :D
Thank you so much for all the help