Thread: What's the idea of trigonometry?

I'm new to trigonometry, and I want to know if this is right.

Being used to algebra, the trigonometric functions seem abstract to me since there are no definite operations.

What I assume: the right triangle model is just a method for defining the functions, correct?

In the function , if I know then I can solve for like this:

Pretend is one of the acute angles in the triangle, and what the ratio for opposite to the hypotenuse will just happen to be . Correct?

So it's not actual operations, just what the ratio will be in this situation?

What do you mean by "actual operations". When you first get exposed to trigonometry, the definitions are given by these ratios - the only "operation" is division.

If you start by being given an angle, then you can get the trig functions by constructing a triangle with the given angle, or look the values up in a table. Implicit in this is the elementary geometry theorem that if two triangles are similar, the ratios of the lengths of corresponding sides are the same.

I know it involves the divisional operation. I should have worded it better. I meant that trigonometry isn't as direct as simple algebra. I see where I was wrong.

So never mind about that. Here's my understanding of the method:

is the ratio of the opposite side to the hypotenuse. Looking at the right triangle model, if I know , then I know all three angle measures.

Therefore, any triangle with these 3 angle measures is similar (or congruent in one situation) to another triangle with the same angle measures.

So, if I had a right triangle where degrees, I know

Since all the triangles are similar, this ratio applies to all sines of . Correct?

The general idea is correct. However sin(30 deg.) = .5 (exactly).

Okay thank you. For some reason I had done the secant.