Spec '10 - Help forum

[superflya]

oh okay

[mandy]

Alright, thanks guys.

[Chavi]

Can I please get some help with the following questions:

1. A circle with centre O and radius, r, is inscribed in a square ABCD. P is any point on the circumference of the circle.
a) Find
b) Hence find in terms of r.

[Martoman]

Can I please get some help with the following questions:

1. A circle with centre O and radius, r, is inscribed in a square ABCD. P is any point on the circumference of the circle.
a) Find
b) Hence find in terms of r.

This is a very_nice_question. This requires a visual proof. Go to this link to see my explanation: http://img169.imageshack.us/img169/5426/proofofsquarecircle.jpg

I'll leave you to do b) now you know where the first part comes from.

EDIT: what the hell, here is the second part, it actually involves a tiny bit of thought so I might as well give it to you.

Link: http://img256.imageshack.us/img256/9340/partb.jpg

[mandy]

Calculate the fourth roots of 100.

So I have :

and then I have no idea what to do.

[TrueTears]

z^4 = 100

Use de moives theorem

Let z = rcis theta

let 100 = 100cis(0)

[mandy]

z^4 = 100

Use de moives theorem

Let z = rcis theta

let 100 = 100cis(0)

Yeah, is there another way to do it without using De Moivre's?

[TrueTears]

You can let z = x+yi

(x+yi)^4 = 100+0i

then equate coefficients


Or factorise

(z^2)^2 - (()^2)^2 use DOPS

[mandy]

Okay, so I used the factorising way, and this is what I got:







So then I get

The answer is meant to be: .
What am I doing wrong here?

[cipherpol]

[mandy]

Thanks a lot guys :]

[TrueTears]

You're welcome xD