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Taximes
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## Posts

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.

LewishamonMugenmidgetonThe 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.

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.

Marty81onThere'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.

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

mrcheesypantsonpretty 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 UponAlso 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 TonSatans..... hints.....

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.

Marty81onBig DookieonOculus: TheBigDookie | XBL: Dook | NNID: BigDookie

enlightenedbumon