what is the smallest interval that will produce a complete graph of r=3sin5Ɵ?
+23246 What is the smallest interval that will produce a complete graph of r=3sin(5x)?
Normally, it takes 360o or 2pi to produce one complete cycle of sin; however, because the function has 5x instead of just x, the graph travels "five times as fast" or it takes only "one-fifth the amount of time to make one full cycle"; thus the smallest interval will be 360o / 5 or 72o; in radians this is 2pi/5.
The '3' in the equation affects the amplitude; the graph's maximum value will be 3 instead of the usual 1; also, the graph's minimum value will be -3 instead of the usual -1.
+118608 I do not understand what you have done Alan. 
If I graph r=3sin(5Ɵ) where r is the vertical axis and theta is the horizontal axis i get an ordinary sine curve.
So what have you done?
Oh the period of this graph is 2pi/5 (in radians) just like geno said.
+33615 I've graphed polar plots Melody. r is the radius and theta is the angle. This is usually what is wanted when an equation is specified using r and theta.
+118608 Thanks Alan,
I don't know about polar plots.
I suppose if I google it I will find a site where I can learn about them......
Got any great ideas?
+33615 Doesn't Desmos allow polar plots? (Just asking - I haven't checked).
If you calculate x = r*cos(theta) and y = r* sin(theta), you should get values of x and y that plot to give the curves I've shown.
+118608 You can do polar graphs with wolfram alpha
but
I don't think you can do polar graphs or enter parametric equations in Desmos. ://
+33615 I've just checked, and Desmos does allow polar plots. If you just use r and theta (use the Greek letter not the word "theta") Desmos automatically assumes you want a polar plot.
+118608 Thanks Alan, I have played with Desmos and have managed to do it.
https://www.desmos.com/calculator/wjcsu3xw4d
I still don't really understand. I guess this gives me some homework to do. ://
