# Thread: Express the lengths in terms of x

1. ## Express the lengths in terms of x

The radius of the circle in the picture provided is one unit. Express the lengths OA, AB, and DC in terms of x.

2. ## Re: Express the lengths in terms of x

Originally Posted by nycmath
The radius of the circle in the picture provided is one unit. Express the lengths OA, AB, and DC in terms of x.
Have you made any effort to solve this? What are the coordinates of point $\displaystyle C~?$
What are the coordinates of point $\displaystyle B~?$
What are the coordinates of point $\displaystyle D~?$

3. ## Re: Express the lengths in terms of x

No coordinates given in the problem. I always make an effort. Please, read my entire signature.

4. ## Re: Express the lengths in terms of x

Originally Posted by nycmath
No coordinates given in the problem. I always make an effort. Please, read my entire signature.
That is not the point! You are to give the coordinates in terms of $\displaystyle x$.

Here is one: $\displaystyle B: (\cos(x), \sin(x))$. That tells you the length of $\displaystyle \overline{BA}$

What are the coordinates of $\displaystyle A~\&~D~?$

5. ## Re: Express the lengths in terms of x

Is the length BA cosx?

Is OA sinx?

Is OB the hypotenuse 1?

I was not able to determine the coordinates for A and D.

6. ## Re: Express the lengths in terms of x

You say 'express the lengths in terms of x' but when your picture shows "x" only as the x-axis, not as a length.

7. ## Re: Express the lengths in terms of x

Originally Posted by nycmath
Is the length BA cosx? Is OA sinx? BACKWARDS

Is OB the hypotenuse 1? CORRECT
I was not able to determine the coordinates for A and D.
$\displaystyle |\overline{BA}|=\sin(x)~\&~|\overline{OA}|=\cos(x) ~$, $\displaystyle |\overline{BA}|$ means length.

And $\displaystyle |\overline{CD}|=\tan(x)$

Can you tell us why?

8. ## Re: Express the lengths in terms of x

Originally Posted by HallsofIvy
You say 'express the lengths in terms of x' but when your picture shows "x" only as the x-axis, not as a length.
Actually the diagram shows that the angle has measure $\displaystyle x$.
It is bad notation, or at least mixed notation.

9. ## Re: Express the lengths in terms of x

Thank you, Plato. I will work on this more on my next day off, which is Monday. This question is from a chapter titled Right-Triangle Trigonometry. A very cool topic.