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Math Question
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Registered User regular
Registered User regular
I've never felt so stupid!
So this is grade ten math shit, but it's been 5 years since I've used it, and now in a second year calc course my prof seems so keen on memorizing this shit that we have to have it memorized.
Anyway, I need help remembering some Trig, in associaiton with the unit circle.
This thing.
Anyway, does anyone have any use tips or tricks to try to re-memorize this thing? I mean, I don't even remember the correlations between sin and cos and tan at these spots.
I mean this is probably the best thing for me to do anyway, to remember this, but damn it came out of nowhere and am not prepared right now to remember basic trig.
Thanks guys, and sorry for the trivial low-level math question.
So this is grade ten math shit, but it's been 5 years since I've used it, and now in a second year calc course my prof seems so keen on memorizing this shit that we have to have it memorized.
Anyway, I need help remembering some Trig, in associaiton with the unit circle.
This thing.
Anyway, does anyone have any use tips or tricks to try to re-memorize this thing? I mean, I don't even remember the correlations between sin and cos and tan at these spots.
I mean this is probably the best thing for me to do anyway, to remember this, but damn it came out of nowhere and am not prepared right now to remember basic trig.
Thanks guys, and sorry for the trivial low-level math question.
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sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
The hypotenuse in the unit circle is always 1.
Therefore, the first value in the coords is the cosine of each degree, and the second value is the sine.
Also, you can just memorize the first (upper left) quadrant and derive the rest.
edit: I guess my problem is, I don't see what the fuck the unit circle is trying to tell me?
If you know pythagoras' theorem, you can derive those two triangles, which will give you the exact values for sin, cos and tan of 30, 60 and 45 degrees.
If you can sketch the graphs of sin, cos and tan, you can figure out the exact values for the multiples as well.
If you can do that, you can draw the unit circle.
In C, only cos is positive. A, all are positive. S = sin, T = tan.
This is true when you measure the angle counterclockwise from y=0 in the first (NE) quadrant.
If you know the unit circle, you can derive the exact values for sin, cos and tan of some common angles without having to look it up or use a calculator. The reason you're being taught it is probably because learning how to derive it all gives you a decent grasp of the principles of trigonometry.
Problem is we can't use calculators, understandably, or else it would ruin the whole having to memorize this, thing.
Sorry guys, I've been reading everything you've said, and I know all of it. The cast rule, SOH CAH TOA, and the 30-60-90 tirangle (1:2:[root3]) and the 45-45-90(1:1:[root2]) but I just can't get it. What is wrong with me? I don't know.
Just to check I guess the point of this is to help derive trig functions, such as cos(0) = 1, sin(0) = 0, right?
And in such a case, if I can draw this circle, I can know that cos(pi/6) = (root3)/2, right?
So lets say I do what Doc says and memorize quadrant 1, then I would use right triangles to derive the other 4 quadrants?
How do I do that? Let's say I know have Q1 memorized and know 2pi/3, and (-1/2 , root3/2).
How would I derive the other quadrants with this info? Maybe an example will burst this bubble of stupidity around me.
Edit: okay I just took another look and I can memorize this thing in a few seconds here now, just noticed a pattern I hadn't looked at before, but I would still like to see an example of deriving other angles by knowing just one quadrant. It would be nice to know what I am missing here.
edit2: memorized, just drew it out, but I didn't use any math other than adding pi/2 as I went through the circle. like I said, would still like to understand how to go from Q1 to Q2, or Q4 using the proper trig methods.
http://id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/projectileMotion/generalSolution/generalSolution.html
You'll notice that they are equivalent to the triangles you are examining in each quadrant. Once you realize that taking the cosine of the angle theta between the hypotenuse and the base just gives you the length of the base directly under the hypotenuse, and that sin theta gives you the vertical projection, you'll be able to tell immediately which values make sense on your unit circle.
For example:
Take your two values for the upper right quadrant at 30 degrees. Obviously the horizontal projection of that hypotenuse (the base of your triangle) is longer than the vertical projection. So your cosine theta value must be greater than your sin theta value.
For 45 degrees they are equivalent.
At 60 degrees, the vertical projection side will be longer than the horizontal, so you say to yourself that the sin theta value must be larger than the cosine theta value.
In this way you only have to memorize the five values and then use common sense. 0, 1, 1/2, rt(2)/2, and rt(3)/2. The signs will be intuitive if you take up and right as positive.
I hope this helps.
haha I like you because this is almost exactly what I did to memorize it. I think this is as far as I need to go for this test I have tomorrow, I'll talk to the teacher sometime this week and do some more practice with trig, because I find my lack of understanding of trig very concerning to me, I used to love math.
Thanks guys, I think this is actually enough for this thread. It can be locked if wanted.