Find the exact value of f(a)+f(a+2pi)+f(a+4pi)

Question

If fx=sinx and f(a)=-(1/9)

Answer 1

Latika, f(x)=sinx has a period of 2pi. This indicates f(x)=f(x+2pi) and f(x+4pi)=f(x+2*2pi)=f(x). Therefore, f(a)=f(a+2pi)=f(a+4pi)=-(1/9)

 

Thus, f(a)+f(a+2pi)+f(a+4pi)=-(1/9)+-(1/9)+-(1/9)=-(3/9)=-1/3

 

Hope this helps.