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# How to find all angles for a given ratio

Maths and statistics discussion, revision, exam and homework help.

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1. Re: How to find all angles for a given ratio
(Original post by Mr M)
Ok, for some reason I was thinking you were Year 12. Why did you choose chem eng over mathematics?
Why did i chose chem eng over maths?

This is very difficult to answer, its due to several reasons.

I have got an A* in A-Level chemistry(AS: 300/300 and A2: 272/300) but still i don't have the same likeness for chemistry as for maths.

Should i consider doing maths?
Can i be a good mathematician? I don't think my maths skills are as good as most of the mathematicians on TSR. May be doing STEP makes them better, right?

What do you think?
2. Re: How to find all angles for a given ratio
A chemical engineering degree is likely to dictate your career path. If you have any doubts, you would be well advised to think about your future now rather than later. STEP certainly sharpens skills but you seem more than capable of reading mathematics from what I have seen.
3. Re: How to find all angles for a given ratio
Presumably you have already applied for and accepted offers though?
4. Re: How to find all angles for a given ratio
(Original post by TenOfThem)
Presumably you have already applied for and accepted offers though?
Yeah, have accepted a few, while am yet to get offers from some universities.

But seriously thinking that my strength lies in maths.
5. Re: How to find all angles for a given ratio
(Original post by TenOfThem)
Presumably you have already applied for and accepted offers though?
Transfers are possible or a gap year might be better than wondering "What if?" for years to come.

My brother-in-law has a chemical engineering degree (third class!) and is now a senior manager for a pharmaceutical company. He is extremely well paid and his only regret is that he has had a lot of trouble with animal rights protestors smashing up his property (he has never has any involvement with animal testing whatsoever but that doesn't seem to matter).
6. Re: How to find all angles for a given ratio
(Original post by Mr M)
general solutions for trigonometry
This ftw.
7. Re: How to find all angles for a given ratio
(Original post by raheem94)
Use the following formulas:

[/latex]
(Original post by Mr M)
What is the CAST diagram if not a rule (and a rule that is seemingly drawn from the aether for the vast majority of students)?
Up in Scotland, all students seem to be taught the CAST diagram. It's a rule that when I did Maths I just accepted on faith, like you said. We weren't shown why it works, I just learned it and applied it. This is the very first time I've seen the list of rules posted as raheem has, I was confused by it at first and that made me stop and think, namely about the graphs of each trig function and I suddenly understand why the rules work.
8. Re: How to find all angles for a given ratio
(Original post by Hype en Ecosse)
We weren't shown why it works, I just learned it and applied it.

Bad teaching does not make a method bad ... all of my students are taught why it works
9. Re: How to find all angles for a given ratio
(Original post by Hype en Ecosse)
Up in Scotland, all students seem to be taught the CAST diagram. It's a rule that when I did Maths I just accepted on faith, like you said. We weren't shown why it works, I just learned it and applied it. This is the very first time I've seen the list of rules posted as raheem has, I was confused by it at first and that made me stop and think, namely about the graphs of each trig function and I suddenly understand why the rules work.
Hooray!
10. Re: How to find all angles for a given ratio
(Original post by TenOfThem)
Bad teaching does not make a method bad ... all of my students are taught why it works
That's very true, I was just trying to make the point that when the rules are laid out in such a manner, compared to the CAST diagram, seem quite self-explanatory.

Those three rules aren't included in the CAST diagram method, at least not in the way I was taught, this may very well be down to bad teaching, too. I just wish maths courses were more geared towards teaching you maths, rather than teaching you to pass the maths exam. The reason these aren't included in the way I was taught is probably because we're only asked to solve ranges of in exams.
It may very well be a problem unique to my teachers, but I still felt like moaning about it.
11. Re: How to find all angles for a given ratio
(Original post by Hype en Ecosse)
That's very true, I was just trying to make the point that when the rules are laid out in such a manner, compared to the CAST diagram, seem quite self-explanatory.

Those three rules aren't included in the CAST diagram method, at least not in the way I was taught, this may very well be down to bad teaching, too. I just wish maths courses were more geared towards teaching you maths, rather than teaching you to pass the maths exam. The reason these aren't included in the way I was taught is probably because we're only asked to solve ranges of in exams.
It may very well be a problem unique to my teachers, but I still felt like moaning about it.
All rules are included in the cast diagram.

Imagine you have cos60, so you will draw a line in the first quadrant where all are positive, so you will get 0.5. Cos is also positive in the 4th quadrant, so you will also draw a line in the 4th quadrant, that makes an angle of 60deg with the horizontal. But as its in the clockwise direction, you will take the angle as negative, which means -60deg.

By the way,
12. Re: How to find all angles for a given ratio
(Original post by raheem94)
All rules are included in the cast diagram.

Imagine you have cos60, so you will draw a line in the first quadrant where all are positive, so you will get 0.5. Cos is also positive in the 4th quadrant, so you will also draw a line in the 4th quadrant, that makes an angle of 60deg with the horizontal. But as its in the clockwise direction, you will take the angle as negative, which means -60deg.

By the way,
Like I said, it was probably just the way I was taught. Each section of the cast diagram only has 1 rule attached to it for us.
If C: 360 - angle
If A: angle
If S: 180 - angle --> this is said to not be valid if the angle is greater than 180
If T: 180 + angle --> also said to not be valid if the angle is greater than 180
Just trying to give an insight into the way I was taught it.

I only included the minus in the plus/minus bit because, as you see above, we're taught the + 180 bit.

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Last updated: April 7, 2012
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