2
votes
1answer
11 views

Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$

Be $S^1$ the unit circle in the plane, that is, $S^1= \lbrace (x,y) : x^2+y^2=1 \rbrace$ with the subspace topology. Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval ...
2
votes
2answers
34 views

Formula for semi circle with diameter up?

So I know the formula for a semi circle is $$y = \sqrt{r^2 - x^2}$$ However, what if I wanted to find the equation for a semi circle who's diameter is at the top of the graph? Would this be the ...
-1
votes
2answers
51 views

What is the equation of the circle which passes through P, Q and R? [closed]

In the diagram, the y-axis is a tangent to the circle. P has co-ordinates (0,2) and Q is (12,2), at angle PRQ it is 90 degrees. HELP PLEASE
2
votes
0answers
40 views

Bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line

Prove, that a bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line. There exists an elementary proof? I know this question can be found here ...
1
vote
2answers
93 views

Preimage of a function

The only way to get better at this sort of thing is to practice, and now I'm also trying to ask myself (and try to answer) more conceptual questions. If a circle with radius $r$ is given in ...
0
votes
2answers
106 views

Question on inverse trig functions and quadrants? Please Help!

Alright, I was doing a question in a book, and it said: $\displaystyle \cos(2x - \frac{\pi}{6}) = \frac{\sqrt{3}}{2}$ I proceeded and got: $\displaystyle 2x - \frac{\pi}{6} = \frac{\sqrt{3}}{2}.$ I ...
2
votes
3answers
10k views

X and Y coordinates of circle giving a center, radius and angle

I have to find the necessary translations in X and Y to move a point 0n a circle to another one. I have a center (X and Y coordinates), a radius, and a current position in radians. And given a value ...
-3
votes
9answers
270 views

Why is $y + x = 3$ not the same as $y^2 + x^2 = 9$

I know this is impossible, but why is the following not possible: $y + x = 3$ is the same as $y^2 + x^2 = 9$ They're meant to be equivalent.
0
votes
1answer
106 views

Function for the upper left part of a circle

What is the function corresponding to the upper left quarter of a circle ? Where $x$ goes from 0 to $x_\text{max}$, and $y=f(x)$ goes from $y_\text{min}$ to $y_\text{max}$.
0
votes
1answer
98 views

Finding a function that computes a point on the unit-circle

I can't find the definition of a function $f(x); x \in [-1;1]$ where $(x|f(x))$ is a point on the unit-circle. Can you please give me a hint? ---------- Edit ----------- Background: I want to ...
2
votes
2answers
373 views

Chord dividing circle , function

Two chords PA and PB divide circle into three parts. The angle PAB is a root of f(x)=0. Find f(x) Clearly , PA and PB divides circle into three parts means it divides it into 3 parts of equal areas ...