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Need Help with Question - HSN forum

# Need Help with Question

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### #1Ron90

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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

### #2Ron90

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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.

### #3Marcus

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Posted 20 January 2008 - 12:19 AM

QUOTE(RM91 @ Jan 19 2008, 04:16 PM)
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 =

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 , 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.

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

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

but, the method would be letting then expand using the compound angle formulae

now, obviously is equal on both sides (same with ) so

and

where

therefore you can find the value of k

now to find the value of you use

=-=-=Marcus=-=-=

### #4Ron90

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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

### #5Steve

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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.
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