Question

Which of the following are equivalent to the function y = 3cOS X + 2? Check all that apply. A. y = 3cos(-x) + 2 B. y = -3cOS X-2 C. y = 3sin(x + 1) +2 + D. y = 3sin(x-7)+2

Answer 1

`y\text{ = 3sin(x + }(\pi)/(2))\text{ + 2 (option C})`

Step-by-step explanation:

We need to plot the graphs of these functions on the same axis:

`\begin{gathered} \text{From the graph, we s}e\text{ the function} \\ y\text{ = 3cosx + 2 has the same grap as } \\ y\text{ = 3sin(x + }(\pi)/(2))\text{ + 2} \\ \\ \text{Please note from angles in trigonometry:} \\ \sin \text{ (90 + }\theta)\text{ = cos }\theta \\ \cos x\text{ = sin (90 + x)} \end{gathered}`

Hence, the correct option

`y\text{ = 3sin(x + }(\pi)/(2))\text{ + 2 (option }C)`