Question

Which of the functions below have period ? Check all that apply.

A. y = tan x
B. y = sec x
C. y = cot x
D. y = csc x

Answer 1

a function will have period if it repeats at regular fixed intervals.
that regular fixed interval will be its period.

Answer 2

so, is there any interval you know of, where sine function repeats itself ?

Answer 3

Sory, I wasn't at my laptop.. so the function repeats?

Answer 4

yes,
sin (x+ 2pi) = sin x
this says that sin function repeats every 2pi radians angle, so
period of sin function T =2pi

Answer 5

since cos is just shifted version of sin (by pi/2), cos will also be periodic with period 2pi

Answer 6

in same way, if you look at graphs, you find that tan (x \(\pm\pi\)) = tan x
so, tan and cot are periodic with period = pi

Answer 7

and sec and cosec are periodic with period 2pi too

Answer 8

in short, all trigonometric functions have period :P

Answer 9

Thanks!

Answer 10

welcome ^_^

Answer 11

I just put up another question.. If you could help that would be great!

Answer 12

y=cot x & y= tan x