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pastpaper 2005 non calc 10b - HSN forum

# pastpaper 2005 non calc 10b

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### #1Sammie

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Posted 03 May 2008 - 02:06 PM

yeah I know your all sick and tired of me by now.

10a) express sin x = - root3 cosx in the form ksin(x-a) where k>0 and 0<=a>=2pie

I got::

sinx - root3 cosx = ksin(x-a)

hence

ksin(x-a) = k (sinxcosa - cosxsina) = ksinxcosa - kcosxsina = kcosasinx - ksinacosx

kcosa = 1 and ksina = root3

so
k = root (3 +1)
k = root 4
k = 2

tana = ksina/kcosa = root3/1 = root3
a = tan-1 (root3) = pie/3

since k = 2 and a = pie/3

sinx - root3cosx = 2sin(x-pie/3)

==> I'm pretty much 100% sure this part is right...

b) sketch y = 3+sinx - root3cosx

from part a
y = 3 + 2sin(x-pie/3)

and it all went sunnyside down from there...I'm pretty much hitting a brick wall with this thing I've had a look at the SQA answers but I have no idea where there getting the numbers from etc

thanks peepsies xo

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