# Trig problem ( i think)

• Dec 23rd 2011, 01:47 AM
TechnicianEngineer
Trig problem ( i think)
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
$\displaystyle 10 = 2x^2(\cos^{2}\theta) + 2y^2(\sin^{2}\theta)$
• Dec 23rd 2011, 02:01 AM
Also sprach Zarathustra
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