Answer: It is the second graph. See the attached figure.
Explanation:
1) You can consider the function y = sin(θ − 2)
as a transformation of the parent function y = sin θ
2) Subtracting a constant from the argument of a function leads to shifting the graph as many units to the right as the constant.
3) So, subtracting 2 from the argument of y = sin θ shifts its graph 2 units to the right.
4) Since the x-intercepts of y = sin θ in the interval 0 to 2π are 0, π, and 2π, the x-intercepts of y = sin(θ − 2)
will be 2, π + 2, and 2π + 2.
5) The x-intercepts are not enough to differentiate between some graphs, so take into account the local maxima or minima.
The local maxima of the function y = sin θ in the interval 0 to 2π are at x = π/2, and 3π/2, then the local maximum of y = sin(θ − 2) is at π/2 + 2.
That is the second graph.
I attach the graph for avoiding confussions.
