Urgent maths help

partyatmygaff

If anyone uses Texts and Tests 4 this is Q.15 on page 73.

Basically this is it

A Triangle is inscribed in a sector of a circle,
centre c, radius r, Θ < 90.
A right angled triangled cad circumscribes the sector, as shown.
If the area of a sector is 1/2r2Θ (One half, r squared, theta) find the area of

A: Triangle cab
B: The sector cab
C: the triangle CAD
Hence show that sin Θ < Θ < tan Θ

As you can guess I am utterly and totally lost. I haven't the faintest idea how to even start to tackle that question.


Edit: My diagram in paint, almost exactly as the book

partyatmygaff

I need this for tomorrow, so anyone if you have even a tip let me know!

partyatmygaff

With a bit of brain churning, I've actually managed to get out A B and C, stuck on the hence part however.

For those interested
A = 1/2 r2 sin (theta) One half r squared sin (theta)
B= One half r squared sin theta
C= one half r squared tan theta

The show Sin theta is less than theta which is less than tan theta which I don't get (Sin Θ < Θ < Tan Θ)

blubloblu

The diagram would help greatly.

partyatmygaff

I actually ended up getting the last part! I will post a diagram later on, just incase anyone else happens to be stuck on a maths question, maybe we can sticky a thread like this with solutions to notoriously difficult maths questions like this from text and tests and concise maths? Anyways

Sin Ø < Ø < tan Ø because

triangle cab's area = ½ r² sinØ
triangle cad's area = ½ r² tanØ

Triangle cad circumscribes cab therefore meaning it is larger in area than cab and as both formulae are the same but for the final section we can prove that tanØ is indeed greater than sinØ.
Hope it helps someone else!

AddictedToYou

Well done for keeping at it!

I went to check could I help but we're only on 2E. Had to finish that section for the weekend and couldn't get Q19. Thought about it for about two minutes, and then gave up.

I'm a terrible person. =P