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exact values qustion... need help!

graham83

Posted 17 January 2011 - 12:01 PM

Recently i've been struggling with exact values questions... wondering if anyone has any handy tips or anything?

The question is:-

What is the exact value of sin(4π/3)?

I realise it might be hard to put up the exact value triangles and stuff but if anyone could take me through it that'd be great thanks...

Marcus

Posted 17 January 2011 - 01:21 PM

Firstly if you look at where 4 [pi]/[_3] is on the graph you'll see that it is in the 3rd quadrant.
Now due to the symmetry of the sin graph, sin(4 [pi]/[_3])=sin(5 [pi]/[_3])= - sin([pi]/[_3])= - sin(2 [pi]/[_3])

From your exact value triangles, the 30 [deg] 60 [deg] one, you can work out that sin(60 [deg])=sin([pi]/[_3]) is [root] 3/2 so therefore sin(4 [pi]/[_3]) must be -[root] 3/2

In these sorts of questions where the angle given isn't on your normal exact value triangles, look at the graph and try to find other angles that you can use.

Hope this helps, if you have any follow up questions just post back :D

graham83

Posted 17 January 2011 - 01:39 PM

View PostMarcus, on 17 January 2011 - 01:21 PM, said:

Firstly if you look at where 4 [pi]/[_3] is on the graph you'll see that it is in the 3rd quadrant.
Now due to the symmetry of the sin graph, sin(4 [pi]/[_3])=sin(5 [pi]/[_3])= - sin([pi]/[_3])= - sin(2 [pi]/[_3])

From your exact value triangles, the 30 [deg] 60 [deg] one, you can work out that sin(60 [deg])=sin([pi]/[_3]) is [root] 3/2 so therefore sin(4 [pi]/[_3]) must be -[root] 3/2

In these sorts of questions where the angle given isn't on your normal exact value triangles, look at the graph and try to find other angles that you can use.

Hope this helps, if you have any follow up questions just post back :D


Great help thanks. Glad i've signed up to the site with help like that at hand.

Thanks again

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