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#1 Ron90

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Posted 19 January 2008 - 04:16 PM

Seems a really simple question, but I can's seem to be able to work it out:


A function f is defined by the formula f(x) = 3x x3.

Find the exact values where the graph of y = f(x) meets the x- and y-axes


Thanks in advance


#2 Ron90

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Posted 19 January 2008 - 04:55 PM

I'm also having problems with this Question:


11. (a) Express f(x) = (sq root)3 cos x + sin x in the form kcos (x a), where k > 0 and
0 < a < pi/2

(b) Hence or otherwise sketch the graph of y = f(x) in the interval 0 ≤ x ≤ 2pi



Thanks again.

#3 Marcus

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Posted 20 January 2008 - 12:19 AM

QUOTE(RM91 @ Jan 19 2008, 04:16 PM) View Post
A function f is defined by the formula f(x) = 3x x3.

Find the exact values where the graph of y = f(x) meets the x- and y-axes


well I'm assuming that x3 = x^{3}

to find when the graph cuts the x-axis you let y = 0 (as all points on the x-axis have y co-ordinates of 0) , so 0=3x-x^{3}, then factorise and solve
[hint: to factorise take out a common factor and then a difference of two squares (make sure you keep your answers as surds here)]
and to find where the graph cuts the y-axis you let x =0 and solve. wink.gif

============

I don't think I can quite explain how to answer your second post... it is better to look at the notes on the hsn site wink.gif

but, the method would be letting \sqrt{3} \cos x + \sin x = k \cos(x-\alpha) then expand using the compound angle formulae

\sqrt{3} \cos x + \sin x = k \cos x \cos \alpha + k \sin x \sin \alpha

now, obviously \cos x is equal on both sides (same with \sin x) so

\sqrt{3} =k \cos \alpha and
1 =k \sin \alpha

where k = \sqrt {\sqrt{3}^{2} + 1^{2}}

therefore you can find the value of k

now to find the value of \alpha you use \tan \alpha = \frac{\sin \alpha}{\cos \alpha}

Finally, state your answer in the form k \cos(x-\alpha)
=-=-=Marcus=-=-=

#4 Ron90

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Posted 20 January 2008 - 02:01 AM

Thanks a lot, its a bit late for me to be thinking about maths right now, so ill try it in the morning smile.gif

#5 Steve

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Posted 22 January 2008 - 06:11 PM

Don't forget our free notes, there are examples of your second question in the notes on Wave Functions. smile.gif
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