Question

Question 3i please http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_s08_qp_3.pdf

Answer 1

I dont get how r=a cosec x

Answer 2

r=a cosec x means that sin x = a/r, right?

....and that comes from the basic geometry of the shape and the fact that sin = opp / adjacent.

if you still can't see it, drop a line from N, parallel to AD, onto AB.

Answer 3

I don't think I'd really think to that extend if this question were to come out during exam. :( Is there any other way besides using cosec?

Answer 4

I would start with
1/2 of the Perimeter of rectangle is 3a+1a = 4a
and this equals the perimeter of the sector: 2r+ rx= r(x+2)
so
r(x+2)= 4a

next, "notice" that a rectangle has parallel sides, so