Question

Could anyone please help me learn how to determine the period of a polar or trigonometric parametric function? What I mean is, how do I determine the point in which the curve start tracing itself again over? Up to what point do I trace the whole curve? Our professor and math tutors suggest using the Calculor Window and increment the Tetha Max, but that is rather inaccurate if we need the exact bounds to find the Surface Area of a Curve. Thank you for your help.

Answer 1

i don't think there is a general method for that. It will depend on your functions. Basicly it will be epressed in terms of sin and cos and their combinations. So you will have to transfor the expression in some way to see it

Answer 2

you can tell by seeing if there is a "slope" in the arguement if its linear

Answer 3

\[a\ trig(mx+b)\]
type thing; the m there would determine the perodicity based on the trig function itself

Answer 4

for sin and cos; 2pi/m

for tan ; pi/m

Answer 5

I see.

Answer 6

For example, we had x = e^sin(tetha) and y = e^cos(tetha) but we had no clue on how to determine the bounds of the integral.

Answer 7

sin cos are bouth periodic, with same period so... 2pi

Answer 8

AS myko states, I was kind of looking for a general rule, but it does seem to be something that is treated in a case by case basis.

Answer 9

yes, trig tends to be very case by case determined :/

Answer 10

But then we had x = cos3(tetha) and y = cos(tetha) and the period was no longer 0 - 2pi.

Answer 11

thats right, couse look: tg =sin/cos also involves sin and cos, like your exponencial, but has period pi, half the sin, cos

Answer 12

so, in the case of the last one, x = cos 3(tetha) and y = cos (tetha); I was thining the period would be 2pi, how would I determine the right one? Thank you

Answer 13

it would be 2pi i guess, couse you would choose the longest of bouth cos3x, cosx

Answer 14

the solutions manual says 0 - pi :s

Answer 15

hmm...
cos3x =cos(2x+x)=cos2xcosx-sin2xsinx = cos^3x-sin^2xcosx -2sin^2xcosx=cos^3x -3sin^2xcosx
maybe you can see it from here....

Answer 16

Here is how I would do it. There may be simpler ways?

Answer 17

@phi this is amazing!!!!!!!!! (exclamation points intended)