Re: Trig problem ( i think)

Quote:

Originally Posted by

**TechnicianEngineer** what is the relationship between x and y

if $\displaystyle x\cos{\theta} + y\sin{\theta} = 1$

and

$\displaystyle x\sin{\theta} - y\cos{\theta} = 3 $

[Ans: x^2 + y^2 = 10]

Solution:

this is my approach

i use reverse engineering to get the correct answer (which is unacceptable):

$\displaystyle 3^2 + 1^2 = (x\cos{\theta} + y\sin{\theta})^2 + (x\sin{\theta} - y\cos{\theta})^2 $

and this is what i get

$\displaystyle 10 = 2x^2(\cos^{2}\theta) + 2y^2(\sin^{2}\theta) $

$\displaystyle 3^2 + 1^2 = (x\cos{\theta} + y\sin{\theta})^2 + (x\sin{\theta} - y\cos{\theta})^2 $

=x^2cos^2(t)+y^2sin^2(t)+x^2sin^2(t)+y^2cos^2(t)=

x^2(cos^2(t)+sin^2(t))+y^2(cos^2(t)+sin^2(t))=

x^2*1+y^2*1