- Trig handout & quiz 4 solutions by Douglas Weathers
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Samuel Pierce
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Douglas Weathers
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Sam Pierce
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Sam Pierce
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Douglas Weathers
- Re: [mat127weathers] Trig handout & quiz 4 solutions by Sam Pierce

- From:
- Douglas Weathers
- Date:
- 2014-03-21 @ 22:09

Now that I've had my fun with the 8:00 quizzes, I've got something I want to address and I don't have any more class time to spend on trig subs. Never write x = a tan x. You're saying that x is a *fixed point *of tangent---that doing tangent to x doesn't change x---but you don't know that's true. The argument of the tangent function must be a different variable (commonly, we use \theta.) Same thing applies to x = a sin x, &c. Otherwise, the quizzes look good. There's a mistake in (2.a), so those of you who took that option got a few extra points thrown your way. Solutions, as well as the trig handout, are available in the Dropbox<https://www.dropbox.com/sh/fzwt4odnaw3qfvk/ZG9NL-C4K-> . Have a good weekend, and good luck on the torus problem (remember that it's centered at (2,0).) Post to this list if you have questions. Best, Douglas.

- From:
- Samuel Pierce
- Date:
- 2014-03-25 @ 01:17

Hi Douglas My question is: Are the exercise questions on the trig pamphlet optional? Sam P. Sent from my iPhone > On Mar 21, 2014, at 6:09 PM, Douglas Weathers <wdweathers@gmail.com> wrote: > > Now that I've had my fun with the 8:00 quizzes, I've got something I want to address and I don't have any more class time to spend on trig subs. > > Never write x = a tan x. You're saying that x is a fixed point of tangent---that doing tangent to x doesn't change x---but you don't know that's true. The argument of the tangent function must be a different variable (commonly, we use \theta.) Same thing applies to x = a sin x, &c. > > Otherwise, the quizzes look good. There's a mistake in (2.a), so those of you who took that option got a few extra points thrown your way. > > Solutions, as well as the trig handout, are available in the Dropbox. > > Have a good weekend, and good luck on the torus problem (remember that it's centered at (2,0).) Post to this list if you have questions. > > Best, > Douglas.

- From:
- Douglas Weathers
- Date:
- 2014-03-25 @ 01:26

Sam, Yes, but not a bad idea if you've got the time and want a better handle on trig. Let me know if you have questions. Best, Douglas. On Mon, Mar 24, 2014 at 9:17 PM, Samuel Pierce <spiercecbhs@gmail.com>wrote: > Hi Douglas > > My question is: Are the exercise questions on the trig pamphlet optional? > > Sam P. > > Sent from my iPhone > > On Mar 21, 2014, at 6:09 PM, Douglas Weathers <wdweathers@gmail.com> > wrote: > > Now that I've had my fun with the 8:00 quizzes, I've got something I want > to address and I don't have any more class time to spend on trig subs. > > Never write x = a tan x. You're saying that x is a *fixed point *of > tangent---that doing tangent to x doesn't change x---but you don't know > that's true. The argument of the tangent function must be a different > variable (commonly, we use \theta.) Same thing applies to x = a sin x, &c. > > Otherwise, the quizzes look good. There's a mistake in (2.a), so those of > you who took that option got a few extra points thrown your way. > > Solutions, as well as the trig handout, are available in the Dropbox<https://www.dropbox.com/sh/fzwt4odnaw3qfvk/ZG9NL-C4K-> > . > > Have a good weekend, and good luck on the torus problem (remember that > it's centered at (2,0).) Post to this list if you have questions. > > Best, > Douglas. > >

- From:
- Sam Pierce
- Date:
- 2014-03-25 @ 02:32

Hi Douglas i do have a couple questions. Is this Torus problem supposed to involve trig subs, or is it using the types of integrals we used on the first exam? Also, can i use a method to find the volume without using integrals, (if I can figure out the best equation) by this I mean the fact that an object has the same volume even after its shape has been changed. (Mainly as an option, I'm still not sure how it will work out). Sam On Mon, Mar 24, 2014 at 9:26 PM, Douglas Weathers <wdweathers@gmail.com>wrote: > Sam, > > Yes, but not a bad idea if you've got the time and want a better handle on > trig. Let me know if you have questions. > > Best, > Douglas. > > > On Mon, Mar 24, 2014 at 9:17 PM, Samuel Pierce <spiercecbhs@gmail.com>wrote: > >> Hi Douglas >> >> My question is: Are the exercise questions on the trig pamphlet optional? >> >> Sam P. >> >> Sent from my iPhone >> >> On Mar 21, 2014, at 6:09 PM, Douglas Weathers <wdweathers@gmail.com> >> wrote: >> >> Now that I've had my fun with the 8:00 quizzes, I've got something I want >> to address and I don't have any more class time to spend on trig subs. >> >> Never write x = a tan x. You're saying that x is a *fixed point *of >> tangent---that doing tangent to x doesn't change x---but you don't know >> that's true. The argument of the tangent function must be a different >> variable (commonly, we use \theta.) Same thing applies to x = a sin x, &c. >> >> Otherwise, the quizzes look good. There's a mistake in (2.a), so those of >> you who took that option got a few extra points thrown your way. >> >> Solutions, as well as the trig handout, are available in the Dropbox<https://www.dropbox.com/sh/fzwt4odnaw3qfvk/ZG9NL-C4K-> >> . >> >> Have a good weekend, and good luck on the torus problem (remember that >> it's centered at (2,0).) Post to this list if you have questions. >> >> Best, >> Douglas. >> >> >

- From:
- Sam Pierce
- Date:
- 2014-03-25 @ 02:34

Douglas, Forgot to add on: What I meant in the last part, was that instead of it being a donut (torus), it would be a cylinder. Sam On Mon, Mar 24, 2014 at 10:32 PM, Sam Pierce <spiercecbhs@gmail.com> wrote: > Hi Douglas > > i do have a couple questions. > > Is this Torus problem supposed to involve trig subs, or is it using the > types of integrals we used on the first exam? > > Also, can i use a method to find the volume without using integrals, (if I > can figure out the best equation) by this I mean the fact that an object > has the same volume even after its shape has been changed. (Mainly as an > option, I'm still not sure how it will work out). > > Sam > > > On Mon, Mar 24, 2014 at 9:26 PM, Douglas Weathers <wdweathers@gmail.com>wrote: > >> Sam, >> >> Yes, but not a bad idea if you've got the time and want a better handle >> on trig. Let me know if you have questions. >> >> Best, >> Douglas. >> >> >> On Mon, Mar 24, 2014 at 9:17 PM, Samuel Pierce <spiercecbhs@gmail.com>wrote: >> >>> Hi Douglas >>> >>> My question is: Are the exercise questions on the trig pamphlet >>> optional? >>> >>> Sam P. >>> >>> Sent from my iPhone >>> >>> On Mar 21, 2014, at 6:09 PM, Douglas Weathers <wdweathers@gmail.com> >>> wrote: >>> >>> Now that I've had my fun with the 8:00 quizzes, I've got something I >>> want to address and I don't have any more class time to spend on trig subs. >>> >>> Never write x = a tan x. You're saying that x is a *fixed point *of >>> tangent---that doing tangent to x doesn't change x---but you don't know >>> that's true. The argument of the tangent function must be a different >>> variable (commonly, we use \theta.) Same thing applies to x = a sin x, &c. >>> >>> Otherwise, the quizzes look good. There's a mistake in (2.a), so those >>> of you who took that option got a few extra points thrown your way. >>> >>> Solutions, as well as the trig handout, are available in the Dropbox<https://www.dropbox.com/sh/fzwt4odnaw3qfvk/ZG9NL-C4K-> >>> . >>> >>> Have a good weekend, and good luck on the torus problem (remember that >>> it's centered at (2,0).) Post to this list if you have questions. >>> >>> Best, >>> Douglas. >>> >>> >> >

- From:
- Douglas Weathers
- Date:
- 2014-03-25 @ 02:41

On Mon, Mar 24, 2014 at 10:32 PM, Sam Pierce <spiercecbhs@gmail.com> wrote: > Is this Torus problem supposed to involve trig subs, or is it using the > types of integrals we used on the first exam? > That type of regimented thinking may not be the way to go. Even though trig subs and u-subs have different names, they are forms of the same move (a change of variables.) A trig sub is definitely involved. Under certain interpretations, so is a u-sub. You're also doing a volume by slicing, hopefully. > Also, can i use a method to find the volume without using integrals, (if I > can figure out the best equation) by this I mean the fact that an object > has the same volume even after its shape has been changed. (Mainly as an > option, I'm still not sure how it will work out). > You're thinking of Cavalieri's principle, and yes, it works here. (Basically, objects with the same number of the same cross-sections have the same volume.) But you're trying to show me how much calculus you've learned, so I'd recommend using integrals.

- From:
- Sam Pierce
- Date:
- 2014-03-25 @ 02:45

Okay I'll go the integral approach, I figured it's work best if I did anyway. Mainly I just wanted to know if that principle works with shapes life Torus's. Thanks, Sam On Mon, Mar 24, 2014 at 10:41 PM, Douglas Weathers <wdweathers@gmail.com>wrote: > On Mon, Mar 24, 2014 at 10:32 PM, Sam Pierce <spiercecbhs@gmail.com>wrote: > >> Is this Torus problem supposed to involve trig subs, or is it using the >> types of integrals we used on the first exam? >> > > That type of regimented thinking may not be the way to go. Even though > trig subs and u-subs have different names, they are forms of the same move > (a change of variables.) A trig sub is definitely involved. Under certain > interpretations, so is a u-sub. You're also doing a volume by slicing, > hopefully. > > >> Also, can i use a method to find the volume without using integrals, (if >> I can figure out the best equation) by this I mean the fact that an object >> has the same volume even after its shape has been changed. (Mainly as an >> option, I'm still not sure how it will work out). >> > > You're thinking of Cavalieri's principle, and yes, it works here. > (Basically, objects with the same number of the same cross-sections have > the same volume.) But you're trying to show me how much calculus you've > learned, so I'd recommend using integrals. >