1. ## Basic Trigonometry Question

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.

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.

3. >>(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.

4. 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.

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

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

6. 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.

7. 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?

8. All Sl**s Take Cash?
That is soo not true...

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

10. 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...

11. 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...

12. Some Old Hippie Caught Another Hippie Tripping On Acid

13. 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.