By shifting the function round by certain angles, it is often possible to find different trigonometric functions that express the result more simply. Some examples of this are given shown by shifting functions round by π/2, π and 2π radians. Because the periods of these functions are either π or 2π, there are cases where the new function is exactly the same as the old function without the shift.

Pedagogy
कोणों के योग और अन्तर की सर्वसमिकाएँ (Angle sum and difference identities)
"cis"
आवर्तता (periodicity)