Delmarstio1991

Okay, okay, I know this is TSF, but it's really the only forum I go to. Anyway, I went to Blackle (variant of Google) to search for the definition of trignometric functions (sine, cosine, tangent, cosecant, etc.) and only found the definitions for the Right Triangle, Unit Circle and Any Circle setting. My book only covers the definitions for the Right Triangle setting. What I need are the definitions for the Any Angle setting and Any Real Number setting. Any help would be appreciated...and if this post becomes more than 1 hour old, consider it no longer valuable.

PS: If this is in the wrong section, then I apologize.

MunkyPhil

Sorry this is late Delmarstio1991. I know it's no use now but here it is for future reference:

On a right angle triangle you have your hypotenuse, opposite and adjacent side. The opposite and adjacent are determined by the angle that you have, the opposite being the side opposite the angle. The trigonometric definitions are then defined as:

Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Secant = 1 / Cosine = Hypotenuse / Adjacent
Cosecant = 1 / Sine = Hypotenuse / Opposite
Cotangent = 1 / Tangent = Adjacent / Opposite.

For any triangle with any angles there are the Sine and Cosine rules in which we define three sides A, B and C with respective opposite angles a, b and c:

Sine Rule - A / Sin(a) = B / Sin(b) = C / Sin(c)

Cosine rule - C^2 = A^2 + B^2 - (2AB x Cos(c))

^2 means to the power of 2 (squared).

Wozer

I've found that a good memory tool to be the following:

cosine = 'close'...i.e. its the adjacent side to the angle...and of course this implies that sine is the opposite side....and yes Virginia I know the definitions of sine and cosine as given above by MunkyPhil....

EnglishPaul

Just as a point of interest, does anybody ever use sec, cosec and cotan for any thing useful?

Delmarstio1991

Bleh...well, thanks anyway.
Still...I was actually going for something a little more in-depth...
Here's what I already knew:

Definitions for Right Triangle:
Sin:Opp/Hyp
Cos:Adj/Hyp
Tan:Opp/Adj
Csc:Hyp/Opp
Sec:Hyp/Adj
Cot:Adj/Opp
Where Opp is the side opposite from the angle theta, Adj is the side adjacent to the angle theta and Hyp is the Hypotenuse.

Definitions for Unit Circle:
Sin:Y
Cos:X
Tan:Y/X
Csc:1/Y
Sec:1/X
Cot:X/Y
Where X is the horizontal distance from the center of the circle and Y is the vertical distance from the center of the circle.

Definitions for Any Circle:
Sin:Y/r
Cos:X/r
Tan:Y/X
Csc:r/Y
Sec:r/X
Cot:X/Y
Where X is the horizontal distance from the center of the circle, Y is the vertical distance from the center of the circle and r is the radius.



So...er...thinking about it, it would still probably be good to know the definitions for the Any Angle setting and Any Real Number setting. So...could someone re-post the definitions in those two settings, in detail?

MunkyPhil

Delmarstio, you've just repeated, albeit in an overly complicated manner (forget about the unit circle), what I said earlier without the any angle rules I gave. The Cosine and Sine rules are for ANY triangle with ANY angles using ANY real numbers. The circle need not be implicated in these because their proof comes from two right angle triangles side by side. Look them up for the proof.

I hope this helps.

EnglishPaul, they're not useful really - just definitions. All the calculus I did just used 1/Cos, 1/Sin and 1/Tan, which is easy enough to deal with using the quotient, product and chain rules.

Delmarstio1991

Sorry for being so late with a response, I don't check my mail all that often. ;;>_>

Anyway, my teacher's just really specific I guess. He considered those definitions to be very different from each other. He actually states that 1/sin is NOT the definition of csc, it's just a consequential proof of the definition of csc that has almost become a part of the definition, but isn't. (like an isosceles triangle which has two congruent sides by definition, but not congruent angles by definition.)
Ah well. Maybe he'll let up on that by the finals at the end of the semester. I hope. <_< >_>

Thanks for the reply though!

beefers1

err... sine/cosine rule... isn't that the same as sine/cosine law?

geeda

find the exact values of the indicated trigonometric functions.wrte fractions in lowest terms.

if an hypotuse is 82,adjacent is 18 and opp 80

yustr

TSF does not help with homework - even old home work. Closed