Question

How many of following statements are true?
(1)Period of $sin\theta$is $pi$, because sin 0 = 0 and $sin\pi =0$,
(2) Period of $cos\theta$ is $\pi$
(3) Period of $tan\theta$ is $\pi$

Answer 1

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 in the domain is important,
So even if $Sin(0+\pi )=Sin0=0,\pi$ can't be the period of Sin x, because
$Sin(x+\pi )=-Sinx\ne Sinx$. If we take $\frac{\pi }{2}$, instead of 0,we get $Sin(\pi +\frac{\pi }{2})=Sin\frac{3\pi }{2}=-1$. This is not equal to $Sin\frac{\pi }{2}$.
The period of Sinx and Cosx is$2\pi$, because $Sin(x+2\pi )$= $Sinx$ and $Cos(x+2\pi )=Cosx.2\pi$ is the fundamental period of these functions. (Fundamental period is the least value of P $(>0)$ for which the function repeats).

Similarly,

Period of tanx is $\pi$ because $tan(\pi +x)=tanx$