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do u knw the graph of cosec x?
One way might be to try rewriting 3csc(2x) as 3/sin(2x). Then from here, mark on your graph where one period should end and where the amplitude should be. Since it's 1/sin it will be "upside down" Look at this picture to give yourself some help along the way so that next time you can see. http://www.wolframalpha.com/input/?i=%203csc(2x)&t=crmtb01 The main points to hit when graphing any trig function are what it looks like at 0, T/4, T/2, 3T/2, and T, since it repeats after that and you can kind of "guess" by filling in the points between where the curve should look like.
i know that cscx = 1/sinx
so if i put that function... 3/sin(2x)?
i can help with an alternate solution ..but for that you need to answer my queries
the graph of csc ..yes i do know what it is!
Find the amplitude and period.
well thats great...now what you need to understand is that the graph of cosec 2x will be same as cosec x only difference is that we have to minimize the graph to t=pi
let me show u how i do that for sin 2x
did you get that ?
sin2x makes the half of sinx
yep similiar is what happens for cosec 2x
its like bending a spring to half its normal position from one side
now ...we are 80% over !
well next step is to increase the magnitude of cosec 2x 3 times
does that mean the maximum is at 3??
think again :)
i mean min 3, max3
okay...so what do i do next?
we actually dont need pencil or paper just our mind to visualize this !!
we are done !! this is ur graph !!
oh yeah!!! omgsh thank you so much!!! wait im gonna do a quick sketch
well see hw elegantmethod it is when compared to normal working that we do mechanically (see kainnui's re[ly)
mark angles pls
is it correct?
exactlyy !! well done !!
Ah thank you so much!!! you're an amzing teacher!!
you did it yourself !! cngrts!!
remember:always use ur visualization power as the first resort to solve math problems..it really simplifies ur work !! good luck!
Yeah, awesome, you're a quick learner Isugano.