Use the graph below to answer the question that follows:
What trigonometric function represents the graph?

f(x) = βˆ’3 sin(x βˆ’ pi over 2)
f(x) = βˆ’3 cos(x βˆ’ pi over 2)
f(x) = 3 cos(x βˆ’ pi over 2)
f(x) = 3 sin(x βˆ’ pi over 2)

Use the graph below to answer the question that follows What trigonometric function represents the graph fx 3 sinx pi over 2 fx 3 cosx pi over 2 fx 3 cosx pi ov class=

Respuesta :

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.

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Answer:

Option

c

Step-by-step explanation:

Given is a graph which has maximum at 3 and minimum at -3.

X intercepts are 0, pi, 2pi and 3pi

Period = 2pi

We know that sin curve has x intercepts as multiples of pi but when there is a phase shift of pi/2 we see that cos curve is the most appropriate

Since amptlitude is 3, and middle line is x axis,

we have y = 3 * trig function with coefficient 1 for x

Hence appropriate function is

f(x) = 3cos (x-pi/2)

Option C would be correct.

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