Why won't you learn your trig stuff?
The most frustrating thing I find as a teacher of A level Maths is that students seem so reluctant to learn trigonometric identities and ratios, e.g. sin(30)=1/2.
Why is this?
Having a really thorough knowledge of "facts" such as these makes questions so much easier. Students often complain about the difficulty of proving trigonometric identities in C3 questions. I'm not surprised by this because they don't have the standard results at their fingertips. It's no use saying "they're in the formula book" because many of them aren't and, even if they were, you wouldn't necessarily be inspired to look for the right thing. For example, if I see sin(x)cos(x) I immediately think of 1/2 sin(2x) Even if the formula for sin(2x) was in the formula book, I don't think you'd make that connection if you hadn't learned it.
Similarly for learning trigonometric values of standard angles. No-one would seriously argue (would they?) that you don't need to learn your times tables, so why be so stubborn about learning trig values? It's true that some calculators give exact answers for these so you don't "need" to learn them, but why spend time faffing about with the calculator when you could be getting on with the question. Calculators can tell you what 6 x 4 is, but it's so much easier if the answer 24 immediately jumps into your head. Isn't it?
Why is this?
Having a really thorough knowledge of "facts" such as these makes questions so much easier. Students often complain about the difficulty of proving trigonometric identities in C3 questions. I'm not surprised by this because they don't have the standard results at their fingertips. It's no use saying "they're in the formula book" because many of them aren't and, even if they were, you wouldn't necessarily be inspired to look for the right thing. For example, if I see sin(x)cos(x) I immediately think of 1/2 sin(2x) Even if the formula for sin(2x) was in the formula book, I don't think you'd make that connection if you hadn't learned it.
Similarly for learning trigonometric values of standard angles. No-one would seriously argue (would they?) that you don't need to learn your times tables, so why be so stubborn about learning trig values? It's true that some calculators give exact answers for these so you don't "need" to learn them, but why spend time faffing about with the calculator when you could be getting on with the question. Calculators can tell you what 6 x 4 is, but it's so much easier if the answer 24 immediately jumps into your head. Isn't it?
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coz we **** be boverd.. duhhhh
Trig identities do seem like this
$£"%^$W^&$*%^EW%$£""%%"£$^%$$
at FIRST as if you can't understand them and it is rock hard to get them stuck in your brain. It does feel at first frightening to look at some identites as if they are another language and jumble
But later on, I guess with a LOT of practice, the identites stay in their minds. Them doing this ton of practice is their responsibility I guess.
For trig ratios have you introduced your students to special triangles? If they avoid using the calculator and actually sketch these triangles and look at them, after a little while, the triangles could just stay in there minds. That's what I did and sooner you can just visualise the triangles instead of writing them out. Then perhaps you immediately know them.
$£"%^$W^&$*%^EW%$£""%%"£$^%$$
at FIRST as if you can't understand them and it is rock hard to get them stuck in your brain. It does feel at first frightening to look at some identites as if they are another language and jumble
But later on, I guess with a LOT of practice, the identites stay in their minds. Them doing this ton of practice is their responsibility I guess.For trig ratios have you introduced your students to special triangles? If they avoid using the calculator and actually sketch these triangles and look at them, after a little while, the triangles could just stay in there minds. That's what I did and sooner you can just visualise the triangles instead of writing them out. Then perhaps you immediately know them.
As a student , I would rather use a Cal to obtain the values. Why should we suffer and commit those ratios to memory...i have no time problems in these maths exams so I don't need to have these ratio values at my fingertips....these ratios are really confusing and I cannot trust my memory...perhaps after some practice in further maths it would by itself become more familiar...
Yes, trig is hard because of those identities......that's the core reason and as long as students do not kill themselves by memorising these random statements, trig would remain difficult. 
Original post by the bear
Young people have no difficulty memorizing hundreds of "pop" songs... so why can't they learn a dozen or so trig relationships ???
Because they are no words. They are random. They have no flow. They give no pleasure. They remind us of failure...
Original post by TheKingOfTSR
Because they are no words. They are random. They have no flow. They give no pleasure. They remind us of failure...
that is a good description of Adele's songs... now what about the trigonometry ?
it ain't relevant to the real world.
where am i gonna use it after the exam?
where am i gonna use it after the exam?
Original post by profmatt
x
Standard angles weren't something I actively tried to learn, they were just something I gradually learnt whilst doing AS maths, I found I had to use the calculator to find the standard angles less and less.
Original post by the bear
young people are expected to challenge so-called "facts".
you say that Cos 60o = 1/2... but maybe it's actually 2/3
you say that Cos 60o = 1/2... but maybe it's actually 2/3
well they can easily verify it themselves
Original post by TheKingOfTSR
Because they are no words. They are random. They have no flow. They give no pleasure. They remind us of failure...
Then make them into a song, I remember we were shown a song at GCSE to help us remember the formulas for the area and circumference of a circle.
[video="youtube;WF3AobS9OTQ"]http://www.youtube.com/watch?v=WF3AobS9OTQ[/video]
Just make one up for trig identities or standard angles, it can't be that hard.
Original post by krisshP
But the thing is memorising trig identities is kinda boring IMO. The fun lies in proving identities, rearranging, logical thinking etc in maths, not much in memorising.
Surely just using them enough will cause you to memorise them, you don't have to actually sit down and repeat them hundreds of times to memorise them.
Original post by the bear
that is a good description of Adele's songs... now what about the trigonometry ?
Same for trig too.
Same for all the maths stuff that's not in the formular booklet.
Original post by profmatt
The most frustrating thing I find as a teacher of A level Maths is that students seem so reluctant to learn trigonometric identities and ratios, e.g. sin(30)=1/2.
Why is this?
Having a really thorough knowledge of "facts" such as these makes questions so much easier. Students often complain about the difficulty of proving trigonometric identities in C3 questions. I'm not surprised by this because they don't have the standard results at their fingertips. It's no use saying "they're in the formula book" because many of them aren't and, even if they were, you wouldn't necessarily be inspired to look for the right thing. For example, if I see sin(x)cos(x) I immediately think of 1/2 sin(2x) Even if the formula for sin(2x) was in the formula book, I don't think you'd make that connection if you hadn't learned it.
Similarly for learning trigonometric values of standard angles. No-one would seriously argue (would they?) that you don't need to learn your times tables, so why be so stubborn about learning trig values? It's true that some calculators give exact answers for these so you don't "need" to learn them, but why spend time faffing about with the calculator when you could be getting on with the question. Calculators can tell you what 6 x 4 is, but it's so much easier if the answer 24 immediately jumps into your head. Isn't it?
Why is this?
Having a really thorough knowledge of "facts" such as these makes questions so much easier. Students often complain about the difficulty of proving trigonometric identities in C3 questions. I'm not surprised by this because they don't have the standard results at their fingertips. It's no use saying "they're in the formula book" because many of them aren't and, even if they were, you wouldn't necessarily be inspired to look for the right thing. For example, if I see sin(x)cos(x) I immediately think of 1/2 sin(2x) Even if the formula for sin(2x) was in the formula book, I don't think you'd make that connection if you hadn't learned it.
Similarly for learning trigonometric values of standard angles. No-one would seriously argue (would they?) that you don't need to learn your times tables, so why be so stubborn about learning trig values? It's true that some calculators give exact answers for these so you don't "need" to learn them, but why spend time faffing about with the calculator when you could be getting on with the question. Calculators can tell you what 6 x 4 is, but it's so much easier if the answer 24 immediately jumps into your head. Isn't it?
Because I've got better things in my life to be getting on with. If I wanted a memory test I would have picked History. (Apologies if History is not actually how I think it is
)There is sufficient time in most exams to work things out. I just finished the second year of my Maths degree and got A* in maths A level, at no point would I have been able to tell you for sure what cos60 is or whatever. (Just ask my teacher
)And the only trig identities I have ever known are cos^2 + sin^2 = 1 , cos(A+B) = cos(A)cos(B) - sin(A)sin(B) and sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
(edited 10 years ago)
What is even more appalling is that some teachers I spoke to can't even recall them trigo stuff at the snap of a finger. Setting real good examples indeed.
Peace.
Peace.
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