Answer:
Step-by-step explanation:
We are to select the correct equation of the given graph.
From the graph, we can see that
y (x = 0) = 1,
y (x = 90°) = 0,
y (x = -90°) = 0,
y (x = 180°) = -1,
y (x = -180°) = -1, etc.
Option (A) is
y=\sin(x+90^\circ).
We have
y(x=0)=\sin(0+90^\circ)=\sin90^\circ=1,\\\\y(x=90^\circ)=\sin(90^\circ+90^\circ)=\cos90^\circ=0,\\\\y(x=-90^\circ)=\sin(-90^\circ+90^\circ)=\sin0^\circ=0,\\\\y(x=180^\circ)=\sin(180^\circ+90^\circ)=-\sin90^\circ=-1,\\\\y(x=-180^\circ)=\sin(-180^\circ+90^\circ)=-\sin90^\circ=-1,~etc.
So, this option is correct.
Option (B) is
y=\cos(x+90^\circ).
We have
y(x=0)=\cos(0+90^\circ)=\cos90^\circ=0\neq 1.
So, this option is not correct.
Option (C) is
y=\sin(x+45^\circ).
We have
y(x=0)=\sin(0+45^\circ)=\sin45^\circ=\dfrac{1}{\sqrt2}\neq 1.
So, this option is not correct.
Option (D) is y=\sin(x+90^\circ).
y=\cos(x+45^\circ).
We have
y(x=0)=\cos(0+45^\circ)=\cos45^\circ=\dfrac{1}{\sqrt2}\neq 1.
So, this option is also not correct.
Thus, the correct option is (A)
