# Peee twoo question...

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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?

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?

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#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?

= 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?

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#3

(Original post by

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?

**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?

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#4

(Original post by

guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas

**TheWolf**)guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas

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**TheWolf**)

guys we need to know p1 formulas too? i have never seen a paper where we really need p1 formulas

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#7

(Original post by

I've been told that you're expected to have P1 knowledge...

**kimoni**)I've been told that you're expected to have P1 knowledge...

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(Original post by

CRAP i cant remember most of the p1 formulas :P

**TheWolf**)CRAP i cant remember most of the p1 formulas :P

I sincerely doubt we'll be asked any sequences and series questions, which contained those AP and GP forumlae...

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(Original post by

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??

**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??

sin(pi - x) expands to sin(pi)cos(x) - cos(pi)sin(x)

and sin(pi) is 0....

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(Original post by

erm no actually sinpi=1, so that goes to cosx as cospi=0

**lgs98jonee**)erm no actually sinpi=1, so that goes to cosx as cospi=0

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#11

(Original post by

sin(pi) is 0, not 1... and cos(pi) is -1, read it through, and it'll make sense!

**kimoni**)sin(pi) is 0, not 1... and cos(pi) is -1, read it through, and it'll make sense!

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(Original post by

ah yes good point..keep think pi radians=90 degrees

**lgs98jonee**)ah yes good point..keep think pi radians=90 degrees

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