How many of following statements are true?
(1)Period of sin θ is π, because sin 0 and sin π = 0
(2) Period of cos θ is π
(3) Period of tan θ is π
Solution: A function f(x) is said to be periodic with period P if f(x+p) = f(x) for all x in the domain of f(x). The last part, for all x the domain is important.
So even if sin (0+π) = sin 0 = 0, π can't be the period of sin x, because
Sin(x+π) = -sin x ≠ sin x. If we take π2, instead of 0, we get sin (π+ π2) = sin 3π2 = -1. This is not equal to sin π2
The period of sinx and cosx is 2π, because sin (x + 2π) = sinx and cos (x + 2π) = cosx. 2π is the fundamental period of these functions. (Fundamental period is the least value of P (>0) for which the function repeats).
Period of tanx is n because tan (π + x) = tan x