Answer:
(C)
Step-by-step explanation:
In order to get the graph of the trigonometric function, we must compare the given function with asin(bx-c)+d and acos(bx-c)+d.
Thus, if we take f(x)= -3sin(x-[tex]\frac{\pi }{2}[/tex]
Comparing this equation with asin(bx-c)+d, we have,
Amplitude (a)=[tex]-3[/tex], b=[tex]1[/tex],c=[tex]\frac{\pi }{2}[/tex] and d=[tex]0[/tex]
Period=\frac{2x}{\left | b \right |} =[tex]2\pi[/tex]
Phase shift =[tex]\frac{c}{b}[/tex] =[tex]\frac{\pi }{2}[/tex] ([tex]\frac{\pi }{2}[/tex] towards right)
Vertical shift= [tex]0[/tex]
Thus, on the basis of these measures, we have the graph.
For f(x)= [tex]-3cos(x-\frac{\pi }{2} )[/tex], comparing with acos(bx-c)+d, we have:
Amplitude= [tex]-3[/tex],
b=[tex]1[/tex],
c=[tex]\frac{\pi }{2}[/tex]
d=[tex]0[/tex]
Period= [tex]2\pi[/tex]
Phase shift= [tex]\frac{\pi }{2}[/tex] ([tex]\frac{\pi }{2}[/tex] toards right)
With these we can draw the graph.
Similarly we can find the variables like above and if we compare all the graphs, we get the result that the graph of [tex]3cos(x-\frac{\pi }{2} )[/tex]= f(x) matches the given graph.
Hence option C is correct.