# librelist archives

## Trig handout & quiz 4 solutions

### Trig handout & quiz 4 solutions

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.

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.
>
>

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.
>>
>>
>

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.
>>>
>>>
>>
>

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.

### Re: [mat127weathers] Trig handout & quiz 4 solutions

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.
>