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Which of the following are equivalent to the function y=3cosx+2? Check all that apply. A. y=3sin(x-π/2)+2
B. y=-3cosx-2
C.y=3sin(x+π/2)+2
D.y=3cos(-x)+2

Respuesta :

A.y=3cos(-x)+2 is correct.
D.y=3sin(x+pi/2)+2 is correct.
On apex.

Answer:

Option C and D are the following equivalent to the function y = 3 cos x+ 2

Step-by-step explanation:

Given the function: y = 3 cos x+ 2

Using trigonometry identities:

For odd/ even identities:

  • sin(-x) =-sin x
  • cos(-x)= cos x

Complementary Angle identities:

  • [tex]\sin x = \cos(\frac{\pi}{2}-x)[/tex]
  • [tex]\cos x = \sin(\frac{\pi}{2}-x)[/tex]

Option A:

[tex]y =3\sin(x-\frac{\pi}{2})+2[/tex]

using trigonometry identity:

[tex]y =3\sin(-(\frac{\pi}{2}-x))+2= -3\sin(\frac{\pi}{2}-x)+2=-3\cos x+2[/tex]

Option B

[tex]y =-3\cos x -2[/tex]

Option C

[tex]y =3\sin(x+\frac{\pi}{2})+2[/tex]         [sin(90 +x) = cos x ]

using trigonometry identity, [sin(90 +x) = cos x ];

[tex]y =3\cos x+2[/tex]

Option D :

[tex]y =3\cos(-x)+2[/tex]        

using trigonometry identity:

[tex]y =3\cos x+2[/tex]

Therefore, the following option which is equivalent to y = 3 cos x+ 2 is C and D



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