glittergal96
Active Member
- Joined
- Jul 25, 2014
- Messages
- 418
- Gender
- Female
- HSC
- 2014
Re: HSC 2015 4U Marathon
Let
![](https://latex.codecogs.com/png.latex?\bg_white (a,b)=(\cos(\theta),\sin(\theta)))
and
![](https://latex.codecogs.com/png.latex?\bg_white (c,d)=(\cos(\phi),\sin(\phi)))
The assumption is then that
![](https://latex.codecogs.com/png.latex?\bg_white ac+bd=\cos(\theta-\phi)=0.)
One way to attain this is by taking
![](https://latex.codecogs.com/png.latex?\bg_white \theta=\phi+\pi/2.)
Then
![](https://latex.codecogs.com/png.latex?\bg_white ab+cd=\sin(\theta+\phi)=\sin(2\phi+\pi/2))
which can take any value in the interval [-1,1].
I really do not think this is the case.There's only one solution for ab + cd
Let
and
The assumption is then that
One way to attain this is by taking
Then
which can take any value in the interval [-1,1].