Basic Trigonometry Question

**xddxogm3** · 01-22-2005

I know you are all wanting to start helping me with my trig.
I have angle theta.
The angel is positive, with the terminal ray in the II quadrant, and passing through the point (-3,4).

I figured out the angel and the triangle sides for the equation. I had a question in regards to the six trigonometric functions.

From the point (-3,4) i understand that the right triangle has sides with lengths of 3, 4 and 5 (r^2=x^2+y^2).

(1) why are the cosine, tangent,cotangent, and secant negative.

I understand that the -3 has to do something with it, but why does the function not used the distance of 3 instead of the coordinate value of -3? are these functions based on position instead of distance?

Sorry if this is confusing, but I am confused on this subject.

**VirtualAce** · 01-22-2005

cosine = adjacent/hypotenuse
cosecant=hypotenuse/adjacent

tangent=opposite/adjacent
cotangent=adjacent/opposite

sine=opposite/hypotenuse
secant=hypotenuse/opposite

That should tell you why you are getting the results you are.

(-3,4) is the origin of the triangle, but that does not play into any of the above functions. All that matters in those trig functions is the 3 sides of the triangle. It could begin at 50000,50000 and still if the lengths are 3,4,5 the sine, cosine, tangent and their respective inverses would not change.

I've shown a triangle here with origin at 3,4, but once you figure out your triange and you know the length of the sides of the triangle, the pythagorean theorem has nothing to do with the origin of the triangle.

I use triangles a lot in 3D programming and while calculating the lengths of the sides of the tri involve vector subtraction the actual trig functions performed on the tri and the pythagorean theorem used to find certain lengths does not.

**Perspective** · 01-22-2005

>>(1) why are the cosine, tangent,cotangent, and secant negative.

Because they are not sin of course

(or cosecant if including inverses.)

there is a rule called the CAST rule which tells you the trig func(s) which are posative in a given quadrent. It looks something like this...

Code:

 S | A
--------
 T | C

where,
C = cos
A = all
S = sin
T = tan
(noting that inverses dont affect the sign, secant and cosecant can be grouped with cos and sin respectively)

The funcion(s) identified in each quadrent is/are always posative in that quadrent.

So, to address your original question... In the second quadrent, sin is posative (making cosecant positive) and everything else is negative.

**VirtualAce** · 01-23-2005

I understand that the -3 has to do something with it, but why does the function not used the distance of 3 instead of the coordinate value of -3? are these functions based on position instead of distance?

I thought that because of this statement the poster didn't understand what was taking place both within the trig functions and within the pythagorean theorem. I'm still lost as to what this statement means.

**The Brain** · 01-23-2005

there is a rule called the CAST rule....

I prefer to think of it as, All Students Take Calculus

**xddxogm3** · 01-23-2005

this book only explains so far how to calculate the trigometric functions.
but it has faild to state what the practical aplications are.
i know the pathagorian therom c^2=b^2+a^2.
this calculates the distance of the third side of the triangle.
i feel that the trigonometric functions are so new to me, that it seems illogical.
i for some unknown reason made an assumption that the trigonometric functions would only deal with positive values, and not negative.
thanks for the help. your answers did fill in some blanks that book left out.

**Lithorien** · 01-23-2005

Originally Posted by The Brain

I prefer to think of it as, All Students Take Calculus

How about, as my teacher put it, All Sl**s Take Cash?

**sean** · 01-23-2005

All Sl**s Take Cash?

That is soo not true...

**xddxogm3** · 01-23-2005

i'm sure some take cards and checks too.
;0)

**sean** · 01-23-2005

We had a cool song in calculus for remembering the quotient rule, set to the tune of the song from Shrek (you know the one Princess Fiano was singing when the bird blew up?)

"lo de hi, less hi de lo, all over low squared!"

Denominator time the derivitive of the numerator, minus the numerator time the derivative of the numerator, etc...

**gcn_zelda** · 01-23-2005

Originally Posted by The Brain

I prefer to think of it as, All Students Take Calculus

That's what my math teacher told us...

I say it's All Students Take Crack, but that's just me personally...

**axon** · 01-23-2005

Some Old Hippie Caught Another Hippie Tripping On Acid

**xddxogm3** · 01-27-2005

This is what i have taken from the post and individual research.

Positive Trigometric Values
"All Sl**s Take Cash"

Code:

II  | I
--------
III | IV

(I) A = all
(II) S = sin/csc
(III) T = tan/cot
(IV) C = sec/cos

I hate to say it, but it's easy to remember and it works.
thanks everybody for your input

**Zach L.** · 01-27-2005

Well, I don't think that phrase is entirely accurate, since the type of person you are refering to expresses a personal trait (a behavior) rather than a profession. I cannot, however, think of a synonym for the profession you are getting at that begins with 'S'.

This concludes my random thoughts for now.

**Thantos** · 01-27-2005

I use the ACTS and move in a clockwise direction, it works for me. I hate trying to remember little ditties. The only one I can remember is for cable color codes primary groups:
Boys On Girls Bring Satsfaction
Blue Orange Green Brown Slate

Thread: Basic Trigonometry Question

Thread Tools

Search Thread

Display

Basic Trigonometry Question

Similar Threads

A basic math programming question

Basic question about GSL ODE func RK4

Basic question about RK4

A very basic question