Higher Mathematics

lightning · 2011-09-08 07:23:17

Uhh, if you don't mind I would like to go over notes I have received from my maths teacher here. I don't quite understand the way she has put them and I sort of need help with my higher maths, so I'll be putting up stuff here almost daily and would appreciate if you could help me with them. :3
Please note that I am a visual learner and don't really benefit from exercises like, learning games and stuff.

'Kay, first up is exact values. I don't really know on how to find the angle? I know it has to do with Basic trig, graphs and the use of the CAST diagram... I think I'm getting confused with finding points on a graph, but anyway, I know there's the triangle involved (I don't know how to read it) and the table, but that's about it.

Any tips? I know this is a must to learn, so that's why I'm starting with it.

bobbym · 2011-09-08 07:31:25

Hi lightning;

Got a link or can you post a diagram?

lightning · 2011-09-08 07:52:57

Forgotten how to do this lol. It's not a manga pic btw it's just what I saved it under for some reason. :3

bobbym · 2011-09-08 07:55:33

Hi;

It looks funny.

lightning · 2011-09-08 07:57:52

Lol, the lighting in my room isn't that good. xD

lightning · 2011-09-08 07:59:52

No idea how √3 = 60° or any of it, really.

(Also no idea how to use the syntax by the way, but bare with me. xD)

bobbym · 2011-09-08 08:01:18

No, I meant would it not look better if it were not sideways?

lightning · 2011-09-08 08:10:37

Last edited by lightning (2011-09-08 08:12:30)

bobbym · 2011-09-08 08:13:30

It is still sideways as you can see.

lightning · 2011-09-08 08:14:05

Oh, idk how to fix it. FAAAAIIILL. I rotated the image but it didn't seem to work.

<URL=http://imageshack.us/photo/my-images/23/manga2003.jpg/><IMG>http://img23.imageshack.us/img23/8239/manga2003.jpg</IMG></URL>

Last edited by lightning (2011-09-08 08:16:43)

bobbym · 2011-09-08 08:21:43

You are using the wrong tags. I am fixing them up for you.

http://imageshack.us/photo/my-images/23/manga2003.jpg

http://img23.imageshack.us/img23/8239/manga2003.jpg

Now you are upside down.

Au101 · 2011-09-08 12:06:10

Hi

I think your diagram is wrong, you can't have a right-angled triangle of sides 1, 2 and √3, like that since

I think that the hypotenuse should be 2 and the side which is currently 2 should be √3.

Last edited by Au101 (2011-09-08 12:09:19)

MathsIsFun · 2011-09-08 12:41:46

May help: Sine Cosine and Tangent in Four Quadrants

Maiya · 2011-09-09 00:21:48

Hello lightning;
what do u want
i mean can u precise about ur question...........

Last edited by Maiya (2011-09-09 22:21:41)

lightning · 2011-09-09 23:32:12

I don't really have a question. ^ It's more understanding of what I'm doing in class. I just need help on how to read the triangles from the picture.

Au101 wrote:

Hi
I think your diagram is wrong, you can't have a right-angled triangle of sides 1, 2 and √3, like that since
I think that the hypotenuse should be 2 and the side which is currently 2 should be √3.

The teacher said that diagram was to help us find the angles, I don't really know how to find the answers and stuff.

I think I may have explained myself wrong... uhh... the triangles are related to sin graphs. Like to find the points of degrees. Does that make sense? There's radians involved too.

I got told that Pi = 180 when doing this. Like, if;

(0≤x≤2(Pi)) = (0≤x≤360°)

It's optional to work in either degrees or radians, but I prefer degrees.

bobbym · 2011-09-09 23:47:45

Hi lightning;

Pi radians is 180°

A radian is about 57.29577951308232°

lightning · 2011-09-13 05:55:28

Oh. Thanks.

How do I read the triangles though?

bobbym · 2011-09-13 06:05:20

Hi

'Kay, first up is exact values. I don't really know on how to find the angle? I know it has to do with Basic trig,

Do you remember SOHCAHTOA?

lightning · 2011-09-13 06:14:37

Yep.

bobbym · 2011-09-13 06:17:36

Hi;

That is really all you need along with pythagoras to do them.
Do you remember how to use SOHCAHTOA.

Macy · 2011-09-13 11:02:32

Hi Lighting,

There are two options for u to choose:

1. The esiest option is memorizing the exact values of table
and applying them to the questions they ask. Then later when you have a bit of understanding
then goes back to work out the exact values of table by yourself.

2. The difficult option is trying to understand where these values come from
That is what the teacher tries to show you.
He/She draw the triangles with the given values-. Then standing at the angle you
find out which side is Opposite, Adjacent in relating to the angle you standing on
then use SOH CAH TOA to work out the values for sin, cos, tan of angle 30, 45,60,90
I hope to make it clearer for you.
Ciao

TMorgan · 2011-09-14 04:11:22

Lightning,
I was also tought these triangles in high school geometry. We were even made to put that chart on a 3x5 index card and keep it handy. Knowing these 2 triangles, the 45-45-90 and the 30-60-90, helps you understand basic trigonometry and the Pythagorean theorem. These triangles are called "right" triangles because they contain a 90 degree angle, which is called a "right" angle. Your handwritten page contains a table of the values and pictures of the 2, labelled "right triangle values". It does contain an error, however. In the 30-60-90 triangle the right angle is between the 1 and sqrt3 sides, not between the 1 and 2 sides. 2 is the hypotenuse (that is the name of the longest side of a right triangle). The right angle is indicated by putting the little square on it. See how you have it on the wrong angle? That is why Au101 said that based on that picture the hypotenuse would be sqrt5 instead of sqrt3.
For the values of the lengths of the sides, by convention the shortest side is given a value of one. This is for consistency.
The term "exact value" I believe refers to the fact that they use the symbols for sqrt2 and sqrt3. This is the only way to exactly describe these values. You could put 1.414 and 1.73 for those values but that is not exact. No matter how many decimal places you use you can never give an exact value for those values except by writing sqrt2 and sqrt3.
Sorry I haven't learned to use the Latex language and print the radical (square root) sign yet.

Au101 · 2011-09-14 04:50:35

Interestingly, TMorgan, to print a square root sign in LaTeX you simply have to use \sqrt, which is similar to what you did

lightning · 2011-09-16 07:20:01

AHH. Oh get it now. Much appreciated, a-thank you. :L

One topic down.

I need help with the ... uhh... I dunno what it's called. But it's like;

g(x) = 1x - 5
f(x) = 4x + 2

And then you've to do f(g(x)).

My problem is subbing it in. My teacher teaches at a fast pace so I've not had time to absort what I have to do so I'm sorry if my descriptions of math are all higglety pigglety.

I know you've to sub it into an equation where there is an "x" but I don't know how to start.

zetafunc. · 2011-09-16 07:24:21

Just take g(x) and substitute that for x in f(x). Like this:

Since g(x) = x - 5, and f(x) = 4x + 2, then

f(g(x)) = 4(x - 5) + 2 = 4x - 20 + 2 = 4x - 18

Do you see what I did there?

Math Is Fun Forum

#1 2011-09-08 07:23:17

Higher Mathematics

#2 2011-09-08 07:31:25

Re: Higher Mathematics

#3 2011-09-08 07:52:57

Re: Higher Mathematics

#4 2011-09-08 07:55:33

Re: Higher Mathematics

#5 2011-09-08 07:57:52

Re: Higher Mathematics

#6 2011-09-08 07:59:52

Re: Higher Mathematics

#7 2011-09-08 08:01:18

Re: Higher Mathematics

#8 2011-09-08 08:10:37

Re: Higher Mathematics

#9 2011-09-08 08:13:30

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#10 2011-09-08 08:14:05

Re: Higher Mathematics

#11 2011-09-08 08:21:43

Re: Higher Mathematics

#12 2011-09-08 12:06:10

Re: Higher Mathematics

#13 2011-09-08 12:41:46

Re: Higher Mathematics

#14 2011-09-09 00:21:48

Re: Higher Mathematics

#15 2011-09-09 23:32:12

Re: Higher Mathematics

#16 2011-09-09 23:47:45

Re: Higher Mathematics

#17 2011-09-13 05:55:28

Re: Higher Mathematics

#18 2011-09-13 06:05:20

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#19 2011-09-13 06:14:37

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#20 2011-09-13 06:17:36

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#21 2011-09-13 11:02:32

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#22 2011-09-14 04:11:22

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#23 2011-09-14 04:50:35

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#24 2011-09-16 07:20:01

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#25 2011-09-16 07:24:21

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