Question

If x=r sinA cos C
y=r sinA sinC
z=r cosA
Prove that r^2= x^2 + y^2 + z^2

Answer 1

$$(x)^2 = (rsinAcosC)^2$$
$$(y)^2 = (rsinAsinC)^2$$
$$(z)^2 = (rcosA)^2$$
and tthme aup
$$(x)^2+(y)^2+(z)^2 = (rsinAcosC)^2+(rsinAsinC)^2+(rcosA)^2$$
$$x^2+y^2+z^2 = r^2sin^2A(cos^2C+sin^2C)+r^2cos^2A$$

Answer 2

$$x^2+y^2+z^2=r^2sin^2A+r^2cos^2A$$
$$x^2+y^2+z^2=r^2(sin^2A+cos^2A)=r^2$$

Answer 3

Thanks a lot for ur detailed solution. Really grateful.

Answer 4

I am a teacher in china. I want to know how old are you?

Answer 5

Good afternoon, Sir. I am 15 yrs old and a student of grade 10 in India.

Answer 6

oh, I know . are you study math yourself ?

Answer 7

Yes, sir.. Our teacher gives a lot of extra problems. I just practice them. Sir, I have to over some 10-11 chapters for Maths Olympiad to be held on Aug 27 here. Can you guide me how to prepare?