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C2 radian question help

Hey this is from jan 06 paper. Got solutions but dont like the way they have done it and I know it can be done another way.

OAB is a sector of a circle radius 5m. The chord AB is 6m long.

a) Show that cos AOB = 7/25

Reply 1

It's just the cos rule- you have a triangle, sides of 5, 5 and 6 and you want one angle.

Reply 2

What solutions are you using?

(Method 1)
Cosine rule.

(Method 2)
Spot a 3-4-5 triangle and use the trig identity cos(2A) = 1 - 2sin^2(A).

cos(AOB)
= 1 - 2sin^2((1/2)AOB)
= 1 - 2(3/5)^2
= 1 - 18/25
= 7/25

Reply 3

OP

I cant get my head round this lol! I did this paper in jan and I know I got it right cause it was show that. I definitely used cos rule though

Reply 4

Jonny W

What solutions are you using?

(Method 1)
Cosine rule.

(Method 2)
Spot a 3-4-5 triangle and use the trig identity cos(2A) = 1 - 2sin^2(A).

cos(AOB)
= 1 - 2sin^2((1/2)AOB)
= 1 - 2(3/5)^2
= 1 - 18/25
= 7/25

Method 1 would have been used. That trig identity is in C3, so presuming knowledge up to C2, candidate would not know to use this method.

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