How Do You Solve a Precalculus Wrapping Function Problem?

[contender569]

Homework Statement

Let W be the wrapping function and suppose f is the real function defined by:
f(theta) = d(W(0), W(pi/2 + theta)) / d(W(0), W(pi/2 - theta))

-Find domain f
-Determine whether f is even, odd, or neither
-Find the zeros of f
-Compute f(theta) in terms of cosine theta and sine theta and simplify the result until it is radical free.

"d" in the equation is the distance.

Homework Equations

The Attempt at a Solution

Could someone help me with solving this problem? I'm aware that I should be doing this myself, but I do not understand it at all and my teacher is not good with explaining things. He doesn't tell us where we can find it in the book, so the book is of no help.

 

[quantumdude]

Well, you've got to show us something. Start by answering these questions:

1.) What is the definition of the wrapping function?

Note that the function value is an ordered pair. Interpret this as a pair of coordinates in the plane (on the unit circle, actually).

2.) What is $W(0)$ (this should be easy, once you answer #1).

3.) Can you find a pair of trig identities to simplify $W(\theta + \pi /2)$?

4.) Using the distance formula, can you simplify the numerator and denominator of $f(\theta )$?

Again, this should be easy once you have #1 answered, provided that you've been given a list of trig identities.

 

[contender569]

My teacher gave us something about the wrapping function, and it says that the function W wraps the real line around the unit circle, so W is called the wrapping function.

I'm not sure if I'm understanding it right, but I think since the radius of a unit circle is 1 and W wraps around the line of the unit circle, W(0) would have the coordinates (1,0).

I'm still trying to figure out #3 and 4, but could you explain what the (0) W(0) is and why exactly it has the coordinates (1,0)?

 

[HallsofIvy]

Learn precise definitions. The "wrapping function" you are talking about assigns. to the number t, the value W(t)= (x,y): where (x,y) is the point you would end at if you started at (1, 0) and measured a distance t around the unit circle. In particular, you should recognise immediately that W($\pi/2$)= (0, 1), W($\pi$)= (-1, 0), W($3\pi/2$)= (0, -1), W($2\pi$)= (1, 0) and W has period $2\pi$.

To determine the simplest form of W($\pi/2+ \theta$) draw a unit circle, mark the point $\pi/2+ \theta$ on that circle (angle $\theta$ past (0, 1)), draw the line from that point to (0,0), draw the line from that point perpendicular to the x-axis, and use trigonometry.