IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: d0ckn3ss on October 11, 2011, 03:49:38 pm

Title: How to solve these types of questions ??
Post by: d0ckn3ss on October 11, 2011, 03:49:38 pm: hi guys... i would like to know how to solve these types of equations

Lets say we have a sector of a circle OAB ( O is the origin)

Radius is 6
Theta= Pie/3

Tangent of Point A and and tangent of point B meet at point X

1) find the length of AX
2) find the area of AXB

now i know that the length arc is r(theta) and area of sector is 1/2(r)^2(theta)
but how do i find out what AX is and the area of AXB ?

and i also attatched another question that is similar
Title: Re: How to solve these types of questions ??
Post by: Arthur Bon Zavi on October 11, 2011, 05:45:01 pm: Solving the attachment.

(5) (i)

OA = OB

(AB)² = (OA)² + (OB)²
(AB)² = (6)² + (6)²
(AB)² = 36 + 36
(AB)² = 72
AB = $\sqrt 72$

AB = OD

angle BAD : tan $\theta$ = $(\frac{opposite}{adjacent})$

tan $\theta$ = 6/6
$\theta$ = tan-1 (6/6)
$\theta$ = 45^o or $(\frac{45}{180})\pi$ = $(\frac{1}{4})\pi$

length of arc : s = r X $\theta$
= $\sqrt 72$ X $(\frac{1}{4})\pi$
= 6.664324407 or 6.67 (correct to 3 significant figures)

(ii)

Area of shaded region = Area of sector ABD - Area of triangle AOB
Area of shaded region = [ $(\frac{1}{2})r^2$ X $\theta$ ] - [ $(\frac{1}{2})$ X b X h] ]
Area of shaded region = [ $(\frac{1}{2})$ X 72 X $(\frac{1}{4} \pi)$ ] - [ $(\frac{1}{2})$ X 6 X 6]
Area of shaded region = 9 $\pi$ - 18
Area of shaded region = 9 ( $\pi$ - 2) = 10.2743338 or 10.3 (correct to 3 significant figures)
Title: Re: How to solve these types of questions ??
Post by: Arthur Bon Zavi on October 11, 2011, 06:12:19 pm: Quote from: d0ckn3ss on October 11, 2011, 03:49:38 pm
Tangent of Point A and and tangent of point B meet at point X

This part is not clear. The tangent can be from any direction and be of any length.
Title: Re: How to solve these types of questions ??
Post by: d0ckn3ss on October 12, 2011, 01:26:16 am: maybee this can help you understand

attached a file