Author Topic: Trig Functions  (Read 2176 times)

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Offline Feather

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Trig Functions
« on: February 02, 2015, 08:08:07 pm »
Just happens to be my luck that I was sick Friday and had a snow day today -- and a math quiz tomorrow, though it may be moved. Also my luck that this happens to be the unit I had trouble with last year, too -- trig functions and the unit circle. Right now I'm just struggling with finding the exact value of expressions without calculators. Having missed the days (and a pretty bad teacher, both this year and last) I didn't get the instruction on this. Basically, it's questions like this:

csc (11π/2) =
sec (-π) =
(sin 45°)(cos 45°) =
sin 405° =
csc 450° =

(Yes I put a lot of them fight me)
So anyone think they could lend me a hand? Paw? Claw? I just need some help with this.
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Offline MessedThoughts

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Re: Trig Functions
« Reply #1 on: February 02, 2015, 09:19:59 pm »
I'm going to assume these answers are in radians cause thats the only way I can think of answering this. I'm hoping that this is what i learned, because i know i have a bit of trig i learn this year but i cant recall for the life of me i this was stuff that was covered last year. If not, then it might be a different procedure

First off, remember that Csc(x) = 1/Sin(x) and Sec(x) = 1/Cos(x). Its the inverse of the Sin/Cos functions. This also means that Csc (x) = Hypotenuse / Opposite for triangles (you know, SOHCAHTOA)

I have no clue what the heck the first two questions are for, because you give an variable with no other information, so i don't know what i'm solving for,

For the following three questions, you will need to remember the radians for the 3 common angles, as well as an ASTC diagram. The first image below shows what an ASTC chart is, basically what that is is a way to visually figure out if you answer is positive or negative in radians. You look along the Y axis for your values if you are using Sin, and the X value if you are looking at Cos. What this chart does is show if you value is positive or negative. A stands for All values in that quadrant are positive, S means all values in that quadrant are positive only for sin. T is for Tan, and S is for Sin.



Now in order to determine the quadrant you are in. You start at the dot, and go counterclockwise, counting each of the degrees. Note that 360 = 0, so you can subtract 360 from any number. As well, negative signs simply mean going clockwise instead of counterclockwise.

Note here, that there are some times for Csc and Sec where you will end up with 0 at the bottom value, which means the answer does not exist

Next, we need to memorize values for radians. There are 3 simple ones you can remember.

for Sin
0 degrees = 0
30 degrees = 1/2
45 degrees = Sqrt(2) / 2
60 degrees = Sqrt(3) / 2
90 degrees = 1
270 degrees = -1

Note that Cos has the values:
60 degrees = 1/2
45 degrees = Sqrt(2) / 2
30 degrees = Sqrt(3) / 2
90 degrees = 0
0 degrees = 1
180 degrees = -1
And are the opposites of Sin, cause thats how grids and the diagram works

As well Tan is Sin/Cos.

Sin/Cos values can easily be determined from these angles, cause you can always figure out based on the quadrant, and then apply the correct modification.

And thats i think all you should need to know, cause there are a few more complex things i dont think you'll be tested on

BTW, answers for the last 3 are:
0.5
Sqrt(2)/2
1

PM ME OR EMAIL ME IF YOU NEED MORE HELP.

Edit: good job me, forgetting the ONLY DIAGRAM IN THE POST
« Last Edit: February 02, 2015, 09:50:37 pm by MessedThoughts »
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Offline Feather

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Re: Trig Functions
« Reply #2 on: February 02, 2015, 09:30:22 pm »
Oops, the symbol in the first two is actually pi, sorry if it looks like "n". Thanks a lot, though!
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Offline MessedThoughts

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Re: Trig Functions
« Reply #3 on: February 02, 2015, 09:41:48 pm »
Oops, the symbol in the first two is actually pi, sorry if it looks like "n". Thanks a lot, though!

Those questions are simple then

Answers for those should be -1 and DNE (does not exist) if i'm doing it in my head right.
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Re: Trig Functions
« Reply #4 on: February 02, 2015, 09:43:41 pm »
Pretty much what MessedThoughts said!

If you need help visualizing it, this diagram will probably help:

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Offline Feather

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Re: Trig Functions
« Reply #5 on: February 02, 2015, 10:49:41 pm »
Screams thanks guys. For some reason I just haven't been able to grasp the whole radians and unit circle thing -- SOH/CAH/TOA stuff I get fine, but dang, my mind just can't seem to wrap itself around a unit circle. Maybe it's just 'cause I'm too stubborn to memorize all those numbers, I don't know. But this helped, at least for tonight. Thanks!
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