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Question

How many of following statements are true?
(1)Period of sin θis pi, because sin 0 = 0 and sin π = 0,
(2) Period of cosθ is π
(3) Period of tanθ is π

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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 in the domain is important,
So even if Sin(0+π)=Sin0=0,π can't be the period of Sin x, because
Sin(x+π)=SinxSinx. If we take π2, instead of 0,we get Sin(π+π2)=Sin3π2=1. This is not equal to Sinπ2.
The period of Sinx and Cosx is2π, 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).

Similarly,

Period of tanx is π because tan(π+x)=tanx


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