The angle theta has its vertex at (0,0), one ray along the positive x-axis and the other ray passing through the point (0,1) what is tan of theta?
a. -1
b. 0
c. 1
d. undefined

undefined.  

Step-by-step explanation:

so there is a point at the origin, and from there there are two rays coming off it.  One goes along the positive x axis, so it goes straight right, then the other goes through point (0,1).  That point is right above the origin.  So it makes an l shape.  what sort of polygon could you fit into the corner of an L?  Well, a square or rectangle, and the corners of a square and rectangle are all 90 degrees is theta.

Now it wants tan of 90 degrees.  tangent is sine divided by cosine, so let's find those.

sine of 90 is the y value on the unit circle at 90 degrees.  Since the unit circle has a radius of 1 then when it points straight up or down the y value is either 1 or -1 respectively.  Similarly cosine is 1 when pointing to the right, at 0 degrees or 360 degrees, and -1 at 180 degrees.  For sine straight up is of course 90 degrees and down is 270 degrees.

Now, sine of 90 is 1 and cosine of 90 is therefore 0.  so now we want sine divided by cosine.  this is 1/0.  Well you can't divide by 0, so it is undefined.