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:
Complementary Angle identities:
- \(\sin x = \cos(\frac{\pi}{2}-x)\)
- \(\cos x = \sin(\frac{\pi}{2}-x)\)
Option A:
\(y =3\sin(x-\frac{\pi}{2})+2\)
using trigonometry identity:
\(y =3\sin(-(\frac{\pi}{2}-x))+2= -3\sin(\frac{\pi}{2}-x)+2=-3\cos x+2\)
Option B
\(y =-3\cos x -2\)
Option C
\(y =3\sin(x+\frac{\pi}{2})+2\) [sin(90 +x) = cos x ]
using trigonometry identity, [sin(90 +x) = cos x ];
\(y =3\cos x+2\)
Option D :
\(y =3\cos(-x)+2\)
using trigonometry identity:
\(y =3\cos x+2\)
Therefore, the following option which is equivalent to y = 3 cos x+ 2 is C and D
