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# [deleted]

Registered User regular
edited July 2022
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Taximes on

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Registered User regular
edited September 2007
Taximes wrote: »
However, I have a dirty secret.

This is your problem. I too, suck at trigonometry naturally (and have since forgotten everything I once knew). However, you just need to go and get help from your TA to begin with, and then the professor. Don't keep it a secret, or it will be assumed you know what's going on, and you tumble further into the rabbit hole.

From what I remember of my own trigonometric fumblings, its about 90% practice and 10% actual aptitude. If you're willing to practice, you can get the handle of almost anything that will be thrown at you.

Head down to the library and get a decent introductory text, and just do an hour a night. The repetition will bang it into your head.

Lewisham on
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Registered User regular
edited September 2007
I personally am still struggling with the fundamentals of Trigonometry like yourself, but it's been recommended to me several times to use flash cards as a sort of self-quiz (blank out parts of the identities and such) and just carry them with me so I can break them out whenever there's a dull moment (not that they'd spice it up or anything).

Mugenmidget on
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Registered User regular
edited September 2007
Taximes wrote: »
Anyway, I have no idea what to do when confronted with a trig function of x when x is an actual value. I can try to visualize the graph, and maybe come up with the right answer if it's really obvious, but I have no idea what the hell anyone is talking about when they whip out a unit circle.

The unit circle is one of the things you should learn, definitely, and how it relates to sin(x)=opp/hyp, etc.

Here's a handy table, for x in degrees.
    x=    0        30        45        60         90
sin x=    0      sqrt(1)/2 sqrt(2)/2 sqrt(3)/2 sqrt(4)/2
cos x= sqrt(4)/2 sqrt(3)/2 sqrt(2)/2 sqrt(1)/2     0


Notice the pattern? I wrote it like that to make the pattern easy to see. Obviously you'll want to simplify things like

sin(30 degrees) = 1/2.

cos(0) = 1, etc.

Marty81 on
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Registered User regular
edited September 2007
So the unit circle (if you need it grab an image of it real fast):

There's a circle of radius one centered at the origin. Declare traveling along the x-axis to be the angle 0. 2 * pi radians is defined as the full rotation around the circle, aka 360 degrees. I assume you knew that stuff, but yaaay background!

Now, for trig:

To figure out what sin/cos x is, travel that angle around the circle. So if x = pi/4, travel 45 degrees along the circle so you end up at the point sqrt(2)/2, sqrt(2)/2. (I'll explain why I know those values specifically momentarily) Once you're there, the cosine value is just the x value of the point, and the sine value is the y value. So then you can figure out the other 4 values from knowing those 2. The tangent is 1, and so forth.

Now, that's the fundamental concept, but where did the values at the point come from?

Well, with a 45 degree angle, if you create the triangle inside the circle with one leg being the x-axis, the hypotenuse being the radius of the unit circle along that angle, and the last leg connecting that radius to the x-axis in a right angle, you get a nice pretty 45-45-90 triangle you probably memorized the properties of in a geometry class. As a refresher, you know the legs are the same length. So x^2 + x^2 = 1 (unit circle, so radius is one), and you can find the legs.

Obviously this is not possible for all angles! So here's the secret of evaluating trig functions by hand: there's not many you can do without a calculator or table. Specifically, the ones you can do (and you should know instantly, and would be expected to on an exam) are the ones with "special" triangles associated with them and multiples of n*pi/4 where n is any integer.

So then if you work through logically:

0 the "triangle" is just the flat line at the x axis, so that's weird, but if you think about it in terms of the coordinates on the unit circle it's easy: (1,0). So the cosine is 1 and sine is 0.

pi/6 gives you a 30-60-90 triangle: so the short leg (the vertical one) is 1/2 the hypotenuse and the longer leg is sqrt(3)/2. So the point is (sqrt(3)/2, 1/2) and the sine and cosine follow from that.

pi/4 I already went through above.

pi/2 is like 0, but now we're going straight up to (0,1).

The rest that you're expected to know are the same as those, but in different quadrants. So for example 2*pi/3 is the "same" as pi/3, but the sign of your cosine is flipped, because you're in the second quadrant, where x is negative.

So there's the general idea of the unit circle, and the idea of how to find the values you can without a calculator. It's really a question of memorization to recall those specific values instantly, but I find it helps me to know where they came from.

Gross simplification: most of the rest of trigs is just knowing and manipulating the identities. Things like the Pythagorean identity you referred to in your post. By dividing through by sine squared or cosine squared you get two new identities that there's no reason to memorize, because they're easily derived. The ones I would remember are things like sin (2x) = 2 sin x cos x and the similar one for cos (2x) that has several variants, one of which is I think 2 cos^2 x - 1.

EDIT: Actual values part beat'd, though don't continue too far with that pattern as it does not continue (or we'd have a sine value outside of [-1,1], which: no.
You can keep going with that, but anytime you hit 1 or -1 when you simplify, reverse the direction you're travelling. So sin 120 is sqrt(3)/2. And when you hit -1 for cosine at 180, go back to -sqrt(3)/2 for cos 210. Also, note it's not a strictly linear relationship (that would be pretty boring, and why would we study it so much?) as there are differing gaps between values of x. But yeah, as long as you keep your x values straight as you extend that chart, it's pretty useful.

enlightenedbum on
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Registered User regular
edited September 2007
The secret to Trig is to memorize the unit circle and those identities you know. Oh and learn the law of sines and cosines if you haven't done so already. If you do all three of those you pretty much know everything you can learn from a high school trig class.

edit: oh and uh.. what enlightenedbum said is good too.

mrcheesypants on
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Oh god. When I was younger, me and my friends wanted to burn the Harry Potter books.

Then I moved to Georgia.
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Registered User regular
edited September 2007
The secret to Trig is to memorize the unit circle and those identities you know. Oh and learn the law of sines and cosines if you haven't done so already. If you do all three of those you pretty much know everything you can learn from a high school trig class.

edit: oh and uh.. what enlightenedbum said is good too.

pretty much yeah

once i memorized that i got so good at it Id stiwtch answers from degrees to radians just to mess with my teacher

nothing quite like her having to pull out her calculator to find the answer for me

I'd Fuck Chuck Lidell Up on
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Do you have enemies then? Good. That means you’ve stood up for something, sometime in your life.Registered User regular
edited September 2007
The secret to Trig is to memorize the unit circle and those identities you know. Oh and learn the law of sines and cosines if you haven't done so already. If you do all three of those you pretty much know everything you can learn from a high school trig class.

edit: oh and uh.. what enlightenedbum said is good too.

Also the two basic 90 degree triangles

The 30,60,90 (sides are SQRT(3), 1 and 2)
and 45,45,90 (1, 1, SQRT(2))

You will never be asked to get any other angles as they just get ridiculous to express in terms of pi().

But really practice.

Additionally since year 9 I have not been without a calculator to use which has full sine values within it. I think you are worrying a bit much about that but it is good to have these funamentals in place.

Blake T on
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Registered User regular
edited September 2007
EDIT: Actual values part beat'd, though don't continue too far with that pattern as it does not continue (or we'd have a sine value outside of [-1,1], which: no.

Right, the chart I posted is not meant to be extended. Rather, finding values outside the chart (like the value of sin(-30 degrees)) can typically be done with the chart together with the unit circle.

Marty81 on
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Smells great! Houston, TXRegistered User regular
edited September 2007
Blaket wrote: »
Additionally since year 9 I have not been without a calculator to use which has full sine values within it. I think you are worrying a bit much about that but it is good to have these funamentals in place.
True, but be careful here. I was not allowed to use a calculator in either my Calc I or Calc II class, and my professor loved trig-related problems. Hopefully most people won't have this problem, but you never know when you might get a sadistic professor like that, or when you might need to figure it out and not have a calculator handy. The guys above me have laid it out pretty well, and it's honestly not too difficult once you practice a bit. Knowing the unit circle and memorizing a few basic trig identities will get you through most problems you have - LOTS of trig identities can be derived quite easily with very basic knowlege, so there's no need to memorize everything. Just know the basics, and know how to derive anything else you might need, and you'll be good.

Big Dookie on
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Registered User regular
edited September 2007
A bonus point calculator wise: don't evaluate! sin(2) is a perfectly valid number. Don't be afraid to use such things in your answer. It's just like sqrt(2) in that sense. When I was grading papers last year for a prof, I much preferred the symbolic root 2 over 1.41 etc. It's prettier that way!

enlightenedbum on
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