Recent content by srfriggen

Hello, I am a high school math teacher and recently presented my students with an intriguing problem: "At any given moment, there are two antipodal points on Earth (180 degrees apart) that have the same temperature." This can be demonstrated using one great circle with two opposite points. If...

I first attempted to find the x and y intercepts, algebraically, and discovered there were none. I then split the equation into y= log(x) - log(x+2) to see if that would give me any insight. It did not. I used a graphing calculator and saw many similarities between x/(x+2) and log((x/(x+2)) but...

Thank you for the reply

The first two equations you wrote do not have the same domains. Consider y=(sqrt(x))^2 and y=x. The former has a domain [0, inf) white the latter is all Reals, even though the equations are both equal.

The denominator of the original fraction becomes zero at the two values I mentioned. I used this fact to solve the equation but then rejected those two values. Should we not take into account the order of operations of the input angle in the original composite function, not the manipulated equation?

When solving for x I get the angles 0, pi, pi/2 and 3pi/2. However, I thought I should reject the pi/2 and 3pi/2 values since they are not in the domain of sec^2(x). I am using the opens tax precalc book and their answer does not reject those two angles.

Why the skeptical face?

I found it! I found what I was envisioning! Check out the gif on the wikipedia site https://commons.wikimedia.org/wiki/File:Cartesian_to_polar.gif#/media/File:Cartesian_to_polar.gif

Hi Dave, Thank you for your reply. It seems you do visually get what I'm saying... another example could be how the curve y = 2+2sin(x) , if wrapped around on itself, would form a cardioid. Can you help to polish up my thoughts? I feel like a simple animation (like a 3blue1brown style...

Ah yes, very true. But do you get what I'm saying about how a cardioid is like a sine curve that's wrapped in a circle?

I'll try to be more clear. If you want the equation, of a line, to look like a line in polar, then you have to use the conversion, as you said. What I'm talking about is, if on the x / y-axis you represent angles on the x-axis, and distance from zero on the y-axis (per usual), then the equation...

Hello, Today I started to think about why graphs, of the same equation, look different on the Cartesian plane vs. the polar grid. I have this visualization where every point on the cartesian plane gets mapped to a point on the polar grid through a transformation of the grids themselves...

Hello, If I wanted to verify tan(x)cos(x) = sin(x), what about when x is pi/2? LHS has a restricted domain so it can't equal sin(x). Does this equation only work with a restricted domain? Nothing in my textbook discusses that. Thank you

Hello, I have attached my question and the work. I believe the answer is correct. Looking for verification. Thank you!

I know what you mean by the principal branch. It's the same reason we restrict the domain for the square root function and call it the principal square root function. But for that function, we do it because we didn't know about imaginary numbers at the time. There are angles in the other branch...