For some purposes it is important to know that any linear combination of sine waves of the same period but different phase shifts is also a sine wave with the same period, but a different phase shift. In the case of a linear combination of a sine and cosine wave, we have

where

More generally, for an arbitrary phase shift, we have

where

and


Implications
कोणों के गुणज के त्रिकोणमित्तीय अनुपात
कोणों के योग और अन्तर की सर्वसमिकाएँ (Angle sum and difference identities)
Linear combinations