# Two little questions relating to pi

• Jun 3rd 2009, 06:58 AM
hopingforhelp
Two little questions relating to pi
I have just finished doing and marking a past paper. I did pretty well but there are two little 3-mark questions which I struggled with:

Question 1
Given that arcsinx = π/6, find x. Find arccosx in terms of π.

Question 2
The curve y = xsin3x crosses the x-axis at P. Find the x-coordinate of P.

According to the examiner's report both of these questions were meant to be simple but quite a few people couldn't understand them. So I would really appreciate if someone could explain in detail how to do each of these questions.

Much Thanx :)
• Jun 3rd 2009, 07:09 AM
yeongil
Quote:

Originally Posted by hopingforhelp
Question 1
Given that arcsinx = π/6, find x. Find arccosx in terms of π.

x would be 1/2 because the sin (π/6) = 1/2. So now, to find arccos (1/2) you need the angle whose cosine is 1/2. The angle would be π/3.

01
• Jun 3rd 2009, 07:42 AM
hopingforhelp
Thanx yeongil but could you please explain why the process involves finding sin (π/6), when the question says arcsinx = π/6, thats the part that confused me when I checked the markscheme.
• Jun 3rd 2009, 09:27 AM
Amer
$arcsinx=sin^{-1}x$

$sin^{-1}x=\frac{\pi}{6}$

$sin(sin^{-1}x)=sin(\frac{\pi}{6})$

$x=sin(\frac{\pi}{6})=\frac{1}{2}$

Quote:

Question 2
The curve y = xsin3x crosses the x-axis at P. Find the x-coordinate of P.
crosses x-axis when y=0 right
so

$xsin(3x)=0$

$x=0....and...3x=n\pi....x=\frac{n\pi}{3}...n... in...N.."natural"$
• Jun 3rd 2009, 02:28 PM
hopingforhelp
Thanx Amer question 1 seems really clear to me now. However for question 2 I have no idea what natural means or does, pls could you explain further. Thanx :)
• Jun 3rd 2009, 02:34 PM
Amer
I mean natural number 1,2,3,4,5,6,.. and so on

cuz sin3x=0

$3x=n\pi$

$sin(0)=0,sin\pi=0,sin2\pi=0,sin3\pi=0,sin4\pi=0... .and... so... on$
• Jun 4th 2009, 05:16 AM
hopingforhelp
Sorry for being slow to catch on but why does 3x = nπ instead of equalling zero?
• Jun 4th 2009, 05:22 AM
Amer
because $3x=n\pi$

contain your solution just sub zero instead of n because sinx=0 have infinite solutions
$0,\pi,2\pi,3\pi,4\pi,5\pi......$

so to take all solutions I said

$3x=n\pi$ this inclusive all solutions for sin3x=0

that's it

it is clear or not ....
• Jun 4th 2009, 06:04 AM
hopingforhelp
Thanx Amer, I think I understand now :)