# Math Help - Definition of Basic Trigonometric Functions

1. ## Definition of Basic Trigonometric Functions

Hello, this is my first post on the forums. I had a question about Sine, Cosine, and Tangent functions. I just started Trigonometry over the summer, so the class moves a little fast. I was hoping if I could get something cleared up from you guys.

Basically, I know how to use these functions, as in I know the basic rules when using them to find angles.

For instance:

Sin x = Opposite/hypotenuse

And so on.

But what does Sine actually mean? I guess what I'm asking, is how would I find the Sine of an angle without a calculator with a sine function? The cosine? I just want to know what's happening when you take the Sine,Cosine, or tangent of something.

Sorry if the questions are elementary.

Thank you,

-Impa

2. Originally Posted by Impalord
Hello, this is my first post on the forums. I had a question about Sine, Cosine, and Tangent functions. I just started Trigonometry over the summer, so the class moves a little fast. I was hoping if I could get something cleared up from you guys.

Basically, I know how to use these functions, as in I know the basic rules when using them to find angles.

For instance:

Sin x = Opposite/hypotenuse

And so on.

But what does Sine actually mean? I guess what I'm asking, is how would I find the Sine of an angle without a calculator with a sine function? The cosine? I just want to know what's happening when you take the Sine,Cosine, or tangent of something.

Sorry if the questions are elementary.

Thank you,

-Impa
questions like this are really broad, and to give it a serious response would be to re-invent the wheel. you should be able to find tons of sites from google that go into the definition of sine and cosine. the other trig functions are just manipulations of those two. so if you learn about those two, you have everything.

you already seem to know their connection to right triangles, so i won't mention that. but to just give you a concise answer: sine and cosine were developed using the unit circle. the points on the unit circle have coordinates of the form $(\cos \theta , \sin \theta )$, where $\theta$ is the angle measured from the positive x-axis. right triangles were drawn on the circle (i'm sure you've seen this before) and the sine and cosine was developed as the ratios you mentioned

3. ## Thanks

Yeah, I figured it was a broad question. I've looked around and found definitions that just went back to the relations. Thank you for your time though!