Graphing Trig Equations

Question

What are the zeros in the interval [0,2pi) of y=sin(x-pi)?

Answer 1

sin(x-pi) = 0

x-pi =--pi, or pi or 0 or pi +npi where n=any integer

x = 0, or pi

x= 0 and pi are the only solutions in the given interval (0, 2pi)

the close parenthesis means the interval does not include the endpoint, 2pi

if the interval had been [0, 2pi] then there would have been 3 solutions

x=0, pi or 2pi

Answer 2

sin (x-pi) = 0

so x - pi must be 0, π, 2π, 3π ...

so x must be π, 2π, 3π ... (adding pi)

So in the interval [0, 2 pi] the zeroes are x = π, 2π