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Author Topic: Water's Urgent Math Methods Question:  (Read 7948 times)  Share 

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Water

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Re: Water's Urgent Math Methods Question:
« Reply #45 on: June 05, 2011, 09:51:36 pm »
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Nooby question


IF we do the modulus of |Cos (x)| between pi < x < 0

Then would the modulus be


Cos (x)   pi/2 < x < 0

and -cos(x)   pi < x < pi/2




:) Would like confirmation, circular functions is one subject that I"m always insecure about
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About Philosophy

When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

jane1234

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Re: Water's Urgent Math Methods Question:
« Reply #46 on: June 05, 2011, 09:55:30 pm »
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Quote from: Water on June 05, 2011, 09:51:36 pm
Nooby question


IF we do the modulus of |Cos (x)| between pi < x < 0

Then would the modulus be


Cos (x)   pi/2 < x < 0

and -cos(x)   pi < x < pi/2




:) Would like confirmation, circular functions is one subject that I"m always insecure about

I think you mean |cos(x)| for 0<x<pi :D

It would be cos(x) for 0<x<pi/2

-cos(x) for pi/2<x<pi

I think that's what you meant, just got your < and > mixed up :P
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moekamo

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Re: Water's Urgent Math Methods Question:
« Reply #47 on: June 05, 2011, 09:58:48 pm »
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yes that is correct :)

something a bit trivial, but your inequalities should be the other way around, like your first one should be 0<x<pi, not pi<x<0, the way you have it, it doesn't make sense, x is greater than pi and less than 0...

EDIT: Beaten :P
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Water

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Re: Water's Urgent Math Methods Question:
« Reply #48 on: June 05, 2011, 10:48:09 pm »
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I"m beginning to realize, there is alot to learn for maths cause, I"m struggling with the itute questions lol.


Given that f(x) = x^2 - 1 , find p such that y = x - 2 is a tangent to y = -f(x-p) -1.
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When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

RobM8

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Re: Water's Urgent Math Methods Question:
« Reply #49 on: June 05, 2011, 11:19:12 pm »
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f(x-p) = (x-p)^2 - 1 = x^2 - 2xp + p^2 - 1
therefore y = -f(x-p) - 1 = 2xp - p^2 - x^2
d/dx(2xp - p^2 -x^2) = 2 - 2x
gradient of y = x - 2 has to equal 2 - 2x for it to be a tangent to y = -(p-x) - 1
solve 1 = 2 - 2x => x = 1/2
hence the graphs intersect at x = 1/2 by the definition of a tangent
when x = 1/2, y = (1/2) - 2 = -3/2
so you have the point (1/2, -3/2)
sub this into y = 2xp - p^2 - x^2
to get -3/2 = p - p^2 - 1/4
then p^2 - p = 5/4
therefore p^2 - p - 5/4 = 0
p = [sqrt(6) + 1]/2 or [-sqrt(6) + 1]/2

tired - hopefully no stupid errors.

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Water

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Re: Water's Urgent Math Methods Question:
« Reply #50 on: June 19, 2011, 01:17:32 am »
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nvm ~ Got it :D
« Last Edit: June 19, 2011, 01:22:53 am by Water »
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When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

Water

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Re: Water's Urgent Math Methods Question:
« Reply #51 on: June 21, 2011, 10:17:40 pm »
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If A is an acute angle such that Tan A = 1, find Tan A/2 ....  Curious on how to solve this, is there some kind of massive manipulation that is required ?
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About Philosophy

When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

b^3

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Re: Water's Urgent Math Methods Question:
« Reply #52 on: June 21, 2011, 10:24:18 pm »
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im guessing the double angle formula?

which is eqiuv to
solve for tan(a/2)
« Last Edit: June 21, 2011, 10:29:24 pm by b^3 »
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HenryP

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Re: Water's Urgent Math Methods Question:
« Reply #53 on: June 21, 2011, 10:25:33 pm »
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Well seeing as they give you Tan A = 1, we can determine that A=pi/4. Then you could probably use the Tan half angle formula to figure out Tan pi/8
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Water

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Re: Water's Urgent Math Methods Question:
« Reply #54 on: June 21, 2011, 10:26:28 pm »
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The answer is (root 2) - 1. If you can show me step by step how to get to that answer, will be great :) To Derive to that answer?

@Henry P, explanation if possible? Or Logical method to get to that answer? Trig is my weakest area in maths, thanks a bunch.

Without a calculator that is perhaps.
« Last Edit: June 21, 2011, 10:28:52 pm by Water »
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b^3

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Re: Water's Urgent Math Methods Question:
« Reply #55 on: June 21, 2011, 10:34:33 pm »
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make it simplier and let x =tan(a/2)
so now you have
rearrange and solve for x


so quadratic formula with positive sol since angle is acute



so then tan(a/2)=
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Water

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Re: Water's Urgent Math Methods Question:
« Reply #56 on: June 21, 2011, 10:35:52 pm »
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Quote from: b^3 on June 21, 2011, 10:34:33 pm
make it simplier and let x =tan(a/2)
so now you have
rearrange and solve for x


so quadratic formula with positive sol since angle is acute



so then tan(a/2)=

Brilliant, thanks for the method :)
« Last Edit: June 21, 2011, 10:37:41 pm by Water »
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About Philosophy

When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

b^3

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Re: Water's Urgent Math Methods Question:
« Reply #57 on: June 21, 2011, 10:45:25 pm »
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No problem, but can you just remind me. do we do the double angle formulas in meth or was that only specialist?
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Water

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Re: Water's Urgent Math Methods Question:
« Reply #58 on: June 21, 2011, 10:51:03 pm »
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Quote from: b^3 on June 21, 2011, 10:45:25 pm
No problem, but can you just remind me. do we do the double angle formulas in meth or was that only specialist?

Dunno, I'll ask teacher on thursday, he just gave the worksheet for our class, and I was like, this looks interesting, so doing it atm :).
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When I see a youth thus engaged,葉he study appears to me to be in character, and becoming a man of liberal education, and him who neglects philosophy I regard as an inferior man, who will never aspire to anything great or noble. But if I see him continuing the study in later life, and not leaving off, I should like to beat him - Callicle

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Re: Water's Urgent Math Methods Question:
« Reply #59 on: June 21, 2011, 10:58:22 pm »
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Pretty sure double angles are not on the study design and is listed as an optional unit in the Essentials textbook.
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