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what is sinx = sin2x

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what is sinx = sin2x

Post  karooomph on Sun Apr 12, 2009 9:32 am

And finally to end my sporadic math question spree...!

what is sinx = sin2x?

how do you solve, and what is the answer?

and i dunno, what unit do you use, radians or degrees? Does one make the question easier than the other?

Thanks again!
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Re: what is sinx = sin2x

Post  bfrsoccer on Sun Apr 12, 2009 1:41 pm

sin x=sin (2x)
sin x=2sin(x)cos(x); identity, based off of sin(a+b) and sin(a-b)
sin x - 2sin(x)cos(x)=0
sin(x)*(1-2cos(x))=0

First case:
1/2=cos(x); now take cos-1, and it doesn't really matter whether you use radians or degrees - I used radians
x=pi/3

Second case:
sin(x)=0
x=0

Then, as sin is periodic, there a bunch of other solutions in the form of [solution, such as x=0]+2pi*[an integer]
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Re: what is sinx = sin2x

Post  karooomph on Sun Apr 12, 2009 5:45 pm

again, couple questions. (I'm really weak at this stuff)

sin x - 2sin(x)cos(x)=0
sin(x)*(1-2cos(x))=0
how'd you get from first line to next?

secondly, you get from (1-2cos(x))=0 to 1/2=cos(x) by dividing 2 to both sides right?
yea, me thinks yes.

so just the first question then.

Thanks
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Re: what is sinx = sin2x

Post  bfrsoccer on Sun Apr 12, 2009 9:41 pm

"how'd you get from first line to next?" I factored out a sin(x). sin(x)*1 - sin(x)*2cos(x)=0

"secondly, you get from (1-2cos(x))=0 to 1/2=cos(x) by dividing 2 to both sides right?" Basically, if you add 2cos(x) to both sides and then divide by 2 that's what you get
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Re: what is sinx = sin2x

Post  karooomph on Mon Apr 13, 2009 11:28 am

Si, si, senior!!! alien

I should've known better and saw that you took sinx out

Gracias muchas!

(btw, no, i dont speak spanish)
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Re: what is sinx = sin2x

Post  albertwilson on Mon Jul 19, 2010 4:52 am

sin2x=sinx
2sinxcosx=sinx
sinx=0 or cosx=1/2
x=0,2pi,pi/3,5pi/3.ANS

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Re: what is sinx = sin2x

Post  LeeRain on Mon Sep 27, 2010 12:00 pm

I should've known better and saw that you took sinx out




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Re: what is sinx = sin2x

Post  nirvana on Tue Nov 02, 2010 3:17 am

Japan says Russia meeting is still on despite Kuril row
File image of Kunashir island, from March 2007 The dispute over the islands has been going on since the end of World War II

Japan's Prime Minister Naoto Kan plans to meet Russian President Dmitry Medvedev later this month, amid renewed tensions in a territorial dispute.

Japan's chief spokesperson Yoshito Sengoku said he believed the meeting at an Asia Pacific summit would go ahead.

Tokyo says it will temporarily recall its ambassador to Russia to hear explanations on the Kuril Islands row.

Mr Medvedev visited one of the four disputed islands on Monday, a move Japan said was "very regrettable".
Continue reading the main story
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* Japan's island row with Russia
* Analysis: Why Kuril dispute will not end any time soon
* Japan, Russia discuss islands row

Japan summoned Russia's ambassador to Tokyo on Monday to express displeasure at the visit.

Moscow called Japan's reaction to the visit "unacceptable".

Russia took control of the islands at the end of World War II; before then, about 17,000 Japanese residents lived in the Kurils.
'Hurt feelings'

The summit of the Asia-Pacific Economic Cooperation set for 13-14 November in Japan may offer a chance for talks however.

"I believe the bilateral meeting will be held," Mr Sengoku said.

The Japanese Economic Minister Banri Kaieda told reporters he was concerned about possible economic repercussions of the row with Russia, over islands located in rich fishing grounds.
map

"Japan and Russia have deep ties when it comes to energy and natural resources development," Mr Kaieda said.

"I am worried about the impact on economic relations from the Russian president's visit to the Northern Territories," he said, using the Japanese name for what Russia calls the Southern Kuriles.

On Monday, Mr Medvedev met local residents in Kunashir, the second-largest of the four islands, and pledged more investment for the region.

He is the first Russian leader to set foot on the islands.

Japanese Foreign Minister Seiji Maehara warned that the visit would "hurt the feelings of the Japanese people".

But Russia's Foreign Minister Sergei Lavrov countered: "It is our land and the Russian president visited Russian land."

The dispute has strained relations between Tokyo and Moscow ever since World War II, preventing the signing of a formal peace treaty.

The islands have rich fishing grounds, mineral deposits and possibly oil and gas reserves.

Mr Medvedev's visit comes as Japan is locked in a separate territorial dispute with another powerful neighbours.

Ties between China and Japan have been strained by a row over islands in the South China Sea - known as Senkaku in Japan and Diaoyu in China - that both claim.







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