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# Peee twoo question... watch

1. Hey.. I'm a bit stuck on this one, don't know what to do:
In the green heinemann book, review ex 2, p.176, question 47

There's a diagram which you might need to see to answer the question, but here's the question anyway

A semicircle, has midpoint O of the diameter AB.
The point P is on the semicircle such that the area of sector POB is equal to the area enclosed by the segment AP

The angle POB is x radians
Prove that x = (1/2)(pi - sin x)

anyone?
2. Area of shaded segment = area of sector AOP - area of triangle AOP

= 1/2(pi - x)r^2 - 1/2(r^2)(sin (pi - x))
= r^2/2 (pi-x - sin (pi-x))

Area of sector POB = 1/2(x)(r^2)

r^2/2 (pi-x - sin (pi-x)) = 1/2(x)(r^2)
pi - x - sin (pi - x) = x
2x = pi - (sin (pi-x))
x = 1/2 (pi - sin x)

I think?
3. (Original post by mik1a)
Area of shaded segment = area of sector AOP - area of triangle AOP

= 1/2(pi - x)r^2 - 1/2(r^2)(sin (pi - x))
= r^2/2 (pi-x - sin (pi-x))

Area of sector POB = 1/2(x)(r^2)

r^2/2 (pi-x - sin (pi-x)) = 1/2(x)(r^2)
pi - x - sin (pi - x) = x
2x = pi - (sin (pi-x))
x = 1/2 (pi - sin x)

I think?
guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas
4. (Original post by TheWolf)
guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas
I couldn't think of any other way.
5. Aah, of course 1/2 ab sin C

Cheers!
6. (Original post by TheWolf)
guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas
I've been told that you're expected to have P1 knowledge...
7. (Original post by kimoni)
I've been told that you're expected to have P1 knowledge...
CRAP i cant remember most of the p1 formulas :P
8. (Original post by TheWolf)
CRAP i cant remember most of the p1 formulas :P
me neither.. Although I've just learnt the circle ones from doing this question.
I sincerely doubt we'll be asked any sequences and series questions, which contained those AP and GP forumlae...
9. (Original post by lgs98jonee)
wot have u done here??have u said that sin(pi-x)=sin x that isnt true is it? or am i missing sumthing simple ??? mik1a have u even done p2 yet? - as in started it at school??
If you havent done P2 you won't get this...
sin(pi - x) expands to sin(pi)cos(x) - cos(pi)sin(x)
and sin(pi) is 0....
10. (Original post by lgs98jonee)
erm no actually sinpi=1, so that goes to cosx as cospi=0
sin(pi) is 0, not 1... and cos(pi) is -1, read it through, and it'll make sense!
11. (Original post by kimoni)
sin(pi) is 0, not 1... and cos(pi) is -1, read it through, and it'll make sense!
ah yes good point..keep think pi radians=90 degrees
12. (Original post by lgs98jonee)
ah yes good point..keep think pi radians=90 degrees
heh, just don't make that mistake in the exam!

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