Periodicity of Trig Functions

Question

Hi! I need help with the following problem:

-Find all values of θ for which sin⁡〖θ=0〗

-What pattern do you observe in the values for θ ?

-Graph the function 〖f(x)=sin〗⁡x on Desmos.com on the interval [-2π,2π] and post a screenshot of the graph. -Where on the graph would you find values of x such that sin⁡x =0 ?

Thank you!

Answer 1

-2pi, -pi, 0, pi, 2pi radians

or

-360, -180, 0, 180, 360 degrees

pattern is the sequence terms are 180 degrees or pi radians apart

. It's an arithmetic sequence with common difference = 180 or pi

a1 = -2pi

a2 = -pi

a3 = 0

a4 = pi

a5 = 2pi

an = a1+(n-1)d

an = -2pi+(n-1)pi where 1 < n < 5

graphically, the solutions are the zeros or x intercepts, the points (-2pi,0), (-pi,0), (0,0), (pi,0), (2pi,0)