Author Topic: Proving Trig Identities/Strategies  (Read 1509 times)

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Offline Subzero

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Proving Trig Identities/Strategies
« on: October 21, 2012, 04:23:23 pm »
Alright let's test out this board :).

Grade level is grade 11 advanced math. I'm having trouble solving a few of these expressions so here they are. x's could be replaced with theta or 'θ' if you wish.

The strategy for this one is apparentally to expand, by the way.
Prove:
a) sin x [sin x + csc x (cos^2 x)] =1

The strategy for this one is supposed to be factoring
Prove:
b) sin x - cos^2 x (sin x) = sin^3 x

Thanks to anyone who responds :)

Also, if this helps:

csc x = 1/sin x

sec x = 1/cos x

cot x = 1/tan x

tan x = sin x/cos x

cot x = cos x/sin x

cos^2 x + sin^2 x = 1 OR cos^2 x = 1 - sin^2 x OR sin^2 x = 1 - cos x

1 + tan^2 x x = sec^2 x

cot^2 x +1 = csc x
« Last Edit: October 23, 2012, 03:34:11 pm by Subzero »
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Offline Will

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Re: Proving Trig Identities/Strategies
« Reply #1 on: October 21, 2012, 05:54:28 pm »
Alright let's test out this board :).

Grade level is grade 11 advanced math. I'm having trouble solving a few of these expressions so here they are. x's could be replaced with theta or 'θ' if you wish.

The strategy for this one is apparentally to expand, by the way.
Prove:
a) sin x (sin x + csc x + cos^2 x) =1

The strategy for this one is supposed to be factoring
Prove:
b) sin x - cos^2 x (sin x) = sin^3 x

Thanks to anyone who responds :)

Also, if this helps:

csc x = 1/sin x

sec x = 1/cos x

cot x = 1/tan x

tan x = sin x/cos x

cot x = cos x/sin x

cos^2 x + sin^2 x = 1 OR cos^2 x = 1 - sin^2 x OR sin^2 x = 1 - cos x

1 + tan^2 x x = sec^2 x

cot^2 x +1 = csc x

Think you are supposed to PM them.
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Offline Subzero

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Re: Proving Trig Identities/Strategies
« Reply #2 on: October 21, 2012, 05:59:48 pm »
I wasn't sure how it worked either but I PMed Nightf0x and he said I could post a thread so yeah.

EDIT: I got the answers yesterday morning. I don't need help anymore.

Prove:
a) sin x [sin x + csc x (cos^2 x)] =1
LS: sin^2 + (sin x)(csc x)(cos^2 x)
sin^2 + (sin x)(1/sinx)(cos^2 x)
sin^2 + cos^2
1 = 1

Prove:
b) sin x - cos^2 x (sin x) = sin^3 x
LS: sin x (-cos^2 + 1)
sin x (sin^2)
sin^3 = sin^3
« Last Edit: October 23, 2012, 03:41:52 pm by Subzero »
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Offline NightF0x

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Re: Proving Trig Identities/Strategies
« Reply #3 on: October 28, 2012, 08:44:41 pm »
Sorry about the SUPER late response (midterms and all @.@). What I like to do to prove these is remember that they're ALL interchangeable. i.e tan(x)=sin(x)/cos(x), etc. Also be sure to memorize important rules such as the law of sines and law of cosines (I had a math teacher when I took precalculus that TROLLED THE HELL out of us with law of sines and cosines). That's pretty much it. Every problem is different and you just need to refer to your trigonometric toolkit and see what you can do. Trig is still my least favorite thing in mathematics, but it's still super important.
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Offline Subzero

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Re: Proving Trig Identities/Strategies
« Reply #4 on: November 05, 2012, 04:47:20 pm »
I won't bother making a new thread every time I post. I'll just post my math questions here if that's alright...

So we're doing sinusodal functions and the question reads:
Below are mapping rules for transformations of y=sinx . Determine the equation in standard form, equation of sinusodal axis, amplitude and period.

a) (x, y) ---> (1/3x - 10°, -2y)

So for standard form, I have y= -2sin3(x+10°). But what's the difference between Standard form and equation of the sinusodal axis? That's my main question. 

Also: Amplitude = 2, Period = 120°
I think... :P

Thank you

Edit: I got the answer. It was simply asking for where the sinusodal axis was located on the graph. So the equation for this one would be y=0. Pretty easy actually, just sounded confusing on the page.
« Last Edit: November 06, 2012, 03:40:31 pm by Subzero »
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Offline Subzero

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Re: Proving Trig Identities/Strategies
« Reply #5 on: December 01, 2012, 07:46:07 pm »
I CHALLENGE someone to try this one. I was smooth sailing until this question but it got me.
.  In an industrial city, the amount of pollution in the air becomes greater during the working week when factories are operating, and then lessens over the weekend.  The number of milligrams of pollutants in a cubic meter of air is given by the following equation where t in the number of days after midnight on Saturday night:
P=40 + [(12sin2π)/7(t-37/12)]

Using this equation, solve for what times during the week the minimum level occurs.

I honestly don't expect any replies on this :P. Lol



Whoops, forgot to edit this. It seems like I'm talking to myself in here but that's okay! XD

But 2π on the unit circle is co-terminal with 0.... soo 12sin(0) will equal zero for the numerator. Zero divded by anything (except zero) will be 0, so therefore P always equals 40. Turns out it was a trick question :P

:staffedit-multi:
« Last Edit: December 07, 2012, 12:49:24 am by Natasha Softpaw »
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