Question

what is period of this function?

Answer 1

\[y=sinx+\cos \pi x\]

Answer 2

but i think its not a periodic function.

Answer 3

period of cosx=2pi
cos2x=2pi/2
cos3x=2pi/3

Answer 4

sinx =pi
cos (pi*x)=2pi/pi

Answer 5

now take there lcm

Answer 6

the period of sin(x) = 2pi
cos(x) = 2pi

so the period for sin(x) + cos(x) is 2pi

but there is a phase shift of pi/4 to the left

just graph it and you'll see the period

https://www.desmos.com/calculator

Answer 7

@ganeshie8.what's your idea about this question?

Answer 8

@k142.help,please.

Answer 9

@nikato.help.

Answer 10

cos(pix) is not equal to cospi(x + 2pi). so the result is that it is not a periodic function.

Answer 11

thank you.