AIBU to ask for help with a Math problem?

[FluffyGoalXXXDX]

DS is doing a distance learning Maths A-Level. He has been staring at this maths problem for the past few hours, unable to make sense of it. He has the answer but can't work out how the problem is to be solved. I have attached a photo of the Maths problem.

Can anyone throw any light on how this Maths problem can be solved?

Thanks in advance for any ideas!

I knew there was a reason I chose not to take maths at A-Level.

I'm glad I was busy playing Sorry! so someone else could solve this nicely.

can he also checkout Khan Academy on youtube etc - great (free) support for maths and other subjects - especially if he's distance learning.

mrwalkensir Thank you for recommending the Khan Academy. I will pass this on. So helpful to have another source of support to tap into!

As a quick hijack - which distance learning company are you using?And would you recommend? My son needs to do A level maths externally next year.
Thanks

Foxranawaywithhisshoes
We are using National Extension College. DS is doing Fastrsck A - Level Maths in one year. NEC have been excellent. The learning materials are really good. His tutor is also fantastic. She marks his assignments a day after he submits them and gives detailed and constructive feedback every time. I can't fault them really. DS is finding it hard squeezing Maths A-level into one year of study. It is a very fast pace and doesn't give much time to absorb the information before you are onto the next topic! He is just about hanging on in there I think.

Can I just salute you maths people. I tell my daughter to ask if you can't understand because you learn that way. Now I didn't understand your solution but I admire you being able to do it and tell someone how.

@Canoo explained it perfectly.

The topic is parametric equations if DS wasn’t sure, coupled with a trig identity. In general, parametric equations tend to be written in terms of t. If the x = and y = are basic expressions (eg x = 2t + 4) then you’d just make t the subject and sub into the y equation. With trig; you can’t do this without encoring arcsin/arccos so instead you use the trig identity to write it in Cartesian form.

Encoring = encountering

To add to Canoo’s post, the question also asks for the ranges of x and y. Now for the given range of theta, cos theta goes from 1/2 up to 1 and down to -1/2 while sin theta goes from -(sqrt3)/2 up to 1 and down to (sqrt3)/2. So the range for x is [1/2,2] and for y is [3-(sqrt3)/2,4], with the square brackets to show that the endpoints are included in the range. This is not a trivial part of the question - you have to look at the values of sin and cos theta throughout the theta-range.

And for those to whom the question is gobbledegook - it is an A level question after all.

The topic is parametric equations if DS wasn’t sure, coupled with a trig identity. In general, parametric equations tend to be written in terms of t. If the x = and y = are basic expressions (eg x = 2t + 4) then you’d just make t the subject and sub into the y equation. With trig; you can’t do this without encoring arcsin/arccos so instead you use the trig identity to write it in Cartesian form.

To add to Canoo’s post, the question also asks for the ranges of x and y. Now for the given range of theta, cos theta goes from 1/2 up to 1 and down to -1/2 while sin theta goes from -(sqrt3)/2 up to 1 and down to (sqrt3)/2. So the range for x is [1/2,2] and for y is [3-(sqrt3)/2,4], with the square brackets to show that the endpoints are included in the range. This is not a trivial part of the question - you have to look at the values of sin and cos theta throughout the theta-range.

There is isn't a single bit of either of those explanations I understood but thank you very much for trying.

The thread title used US English (math instead of maths), so YABU.

here are the equations coded in Matlab and a plot of the results. you can read the ranges for X and Y off the plot to check what the text book says

Propagandalf The thread title used US English (math instead of maths), so YABU

It was actually a typo. I was really annoyed with myself when I reread my OP!

GivenchyDahhling, Actoncurrerellis, Allaboardthemagicbus2020 and parietal
Wow. Thank you for these amazingly detailed and helpful explanations! Much appreciated.

@parietal

Yep, still no clearer.

I got an A at A level maths. Swaggered in here feeling pretty confident in my ability to help.
Yeah, not a fucking clue

This thread has given me palpitations

@DropYourSword
@DesLynamsMoustache

Yep. Feeling completely dense now. Tried to work it out and came up with -2 as the answer.

Not even sure how I got that.

Allaboardthemagicbus2020 basically what it's asking you to do is eliminate the theta, so instead of an equation telling you what x is in terms of theta, and another telling you what y is in terms of theta, you end up with just one equation relating x and y directly.

@MereDintofPandiculation

So where does pie come into it? And what s with the colon and the underscored less than symbol?

#missedlotsofmathsatschool

That's the wrong pie isn't it? Pi

Pi = squiggly symbol = 3.14

@Allaboardthemagicbus2020 It’s radian measure, it’s defining the range of the equation so instead of degrees it’s measured in pi. 2pi is the equivalent of 360 degrees so fractions of pi are therefore the degree equivalent.

So if you type eg sin 30 into a calculator in degree mode you get 0.5. If you type sin (pi/6) into a calculator in radian mode you also get 0.5.