# How it works...

• May 14th 2008, 06:52 PM
Ruckamongus
How it works...
First of all, this is my first day on the forums, so I sincerely apologize if this topic is in the wrong section. Now to the reason of this topic. I have used google and wikipedia, but I still don't understand sin, cos, and tan. I would greatly appreciate it if somebody would explain them in english to me, I want to understand them more thouroghly. Thank you for your time.
• May 14th 2008, 09:01 PM
Mathstud28
Quote:

Originally Posted by Ruckamongus
First of all, this is my first day on the forums, so I sincerely apologize if this topic is in the wrong section. Now to the reason of this topic. I have used google and wikipedia, but I still don't understand sin, cos, and tan. I would greatly appreciate it if somebody would explain them in english to me, I want to understand them more thouroghly. Thank you for your time.

I am assuming you mean you want them described geometrically not analytically. If not say so.

In a right triangle, there are three sides, these sides are based upon which angle you reference yourself from. Two sides are variable, one is not.

No matter where you reference yourself the hypoteneuse(deonted h) is always the same, but the opposite(denoted o) and the adjacent(denoted a) sides change depending from which angle you are working off of.

These three functions you speak of are geometrically defined as the RATIO between the sides of a right triangle. So for example

$\cos(\theta)=\frac{a}{h}$

This means that the cosine of the angle you are at is the decimal representation of the ratio between the hypoteneuse and the side opposite of your angle..

$\sin(\theta)=\frac{o}{h}$

Or in other words a decimal represenation of the ratio between the two sides

and finally $\tan(\theta)=\frac{o}{a}$

This is the same thing as the others but for different sides
• May 15th 2008, 03:45 AM
angel.white
Quote:

Originally Posted by Mathstud28
No matter where you reference yourself the hypoteneuse(deonted h) is always the same, but the opposite(denoted o) and the adjacent(denoted a) sides change depending from which angle you are working off of.

To clarify this slightly, the hypotenuse can and does change, but because the trigonometric functions are a ratio, the change is not reflected in an answer.

Think of how 1/2 and 10/20 are the same.

Try applying what Mathstud said, can you find sine, cosine, and tangent for the triangles in the image I'm attaching? (on letter f, try to find the lengths of the other two sides of the triangle. Let $\theta = \frac{\pi}4$ which is another way of saying 45º think about what sine and cosine mean algebraically, then think about how you would find the variable you are looking for)
• May 15th 2008, 04:41 AM
CaptainBlack
Quote:

Originally Posted by Mathstud28
In a right triangle, there are three sides, these sides are based upon which angle you reference yourself from. Two sides are variable, one is not.

No matter where you reference yourself the hypoteneuse(deonted h) is always the same, but the opposite(denoted o) and the adjacent(denoted a) sides change depending from which angle you are working off of.

These three functions you speak of are geometrically defined as the RATIO between the sides of a right triangle. So for example

$\cos(\theta)=\frac{a}{h}$

This means that the cosine of the angle you are at is the decimal representation of the ratio between the hypoteneuse and the side opposite of your angle..

Cosine is the adjacent over the hypotenuse. Sine is the opposite over the hypotenuse. Tangent is opposite over adjacent.

(and representation as a decimal, a common fraction, hexadecimal, binary, ... is irrelevent here)

RonL
• May 15th 2008, 06:27 AM
angel.white
Quote:

Originally Posted by angel.white
To clarify this slightly, the hypotenuse can and does change, but because the trigonometric functions are a ratio, the change is not reflected in an answer.

Think of how 1/2 and 10/20 are the same.

I want to expound on this slightly. The trigonometric functions are very closely tied to the unit circle. On the unit circle, the hypotenuse is defined as "1" this is because the hypotenuse is the same as the radius of the circle, and the radius is defined as "1" (hence the name "unit") so on the unit circle, the hypotenuse does not change.