How can we generate an orthogonal sinusodial signal to any other signal?

I have three signals which are \begin{align} A&=\cos\left(2\pi ft + \frac \pi2\right)\\ B&=\cos\left(2\pi ft\right)\\ C&=\cos\left(2\pi ft + \frac {5\pi}4\right) \end{align}

What i need to do is to draw two orthogonal sinusoidal signal D and E which are also orthogonal to the previous three. That is, D and E will be orthogonal to each other and they will be orthogonal with A, B and C too, at the same time. There is no constraint on the carrier frequency. How can i do it?

• hm. Somethings strange here – what's the definition of orthogonality, and how do you apply it to $B$ and $C$? – Marcus Müller Apr 9 at 22:20
• Why do you "need" to do this? What is the application? – Hilmar Apr 9 at 22:51
• It's my homework actually, ahaha :'( – cetin Apr 9 at 22:55
• sinsusoids which are not same frequency are orthogonal which is the foundation for foueir series. – Ch.Siva Ram Kishore Apr 10 at 2:44
• A and B are orthogonal but C is not orthogonal to either A or B; that said I take it your title is misleading as it would mean all signals A, B, C, D and E should be orthogonal to each other which can't be the case. – Dan Boschen Apr 10 at 14:02