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 Β 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.