Sorry for the vague title, but I'm not sure what to call it.

I have a series of questions based on the above figure, but I'm not sure how to look at it. It asks to state the value of certain trigonometric ratios.

First one is $\displaystyle Sin \theta$, and the answer in the back of the book is $\displaystyle b$. I'm not sure how they got just $\displaystyle b$ as I would have thought it to be $\displaystyle \displaystyle \frac{y}{r}$ for sin.

If anyone could help me read the figure/answer one of the questions so I could finish it off, I would greatly appreciate it!

2. as I would have thought it to be $\displaystyle \displaystyle \frac{y}{r}$ for sin.
That is absolutely correct.
But also notice that $\displaystyle r=1$, look at the diagram.
$\displaystyle \displaystyle \frac{b}{1}=b$

3. Originally Posted by Plato
That is absolutely correct.
But also notice that $\displaystyle r=1$, look at the diagram.
$\displaystyle \displaystyle \frac{b}{1}=b$
How do you know $\displaystyle r=1$?

4. Originally Posted by IanCarney
How do you know $\displaystyle r=1$?
Look at the diagram.
That is the unit circle.
Center at $\displaystyle (0,0)$ and contains the point $\displaystyle (1,0)$.
So the radius is $\displaystyle r=1$.

5. Originally Posted by Plato
Look at the diagram.
That is the unit circle.
Center at $\displaystyle (0,0)$ and contains the point $\displaystyle (1,0)$.
So the radius is $\displaystyle r=1$.
But I thought we were using the point $\displaystyle (a,b)$ and not $\displaystyle (1,0)$? Or does that not matter (I assumed that the radius would be different)?

6. Originally Posted by IanCarney
But I thought we were using the point $\displaystyle (a,b)$ and not $\displaystyle (1,0)$? Or does that not matter (I assumed that the radius would be different)?
A circle is a set of points that are all equally distant, the radius, from a fixed point, the center. So every point on that circle is one unit from $\displaystyle (0,0)$.

Thus $\displaystyle r^2=a^2+b^2=1~!$