Let's put more details in the given graph:
For us to be able to determine the equation of the given graph, we will be applying the following formula:
[tex]\text{ y = A }\cdot\text{ Cos \lparen Bx + C\rparen + D}[/tex]
Where,
A = Amplitude
B = 2π/Period
C = Phase Shift
D = Vertical Shift
Let's determine their values.
A = Amplitude
[tex]\text{ Amplitude = }\frac{\text{ y}_{Max}\text{ - y}_{Min}}{2}\text{ = }\frac{1\text{ - \lparen-1\rparen}}{2}\text{ = }\frac{1\text{ + 1}}{2}\text{ = }\frac{2}{2}\text{ = 1}[/tex]
Therefore, the Amplitude is 1.
B = 2π/Period
[tex]\text{ Period = }\frac{2π}{B}[/tex][tex]\text{ \pi = }\frac{2π}{B}[/tex][tex]\text{ B = }\frac{2π}{π}[/tex][tex]\text{ B = 2}[/tex]
Therefore, B = 2
C = Phase Shift
[tex]\text{ C = Phase Shift = 0}[/tex]
D = Vertical Shift
[tex]\text{ D = Vertical Shift = 0}[/tex]
In Summary, we have A = 1, B = 2, C = 0 and D = 0.
Let's now plug it to the formula to get the equation of the graph.
[tex]\text{ y = A }\cdot\text{ Cos\lparen Bx + C\rparen + D}[/tex][tex]\text{ y = \lparen1\rparen }\cdot\text{ Cos\lparen\lparen2\rparen x + 0\rparen + 0}[/tex][tex]\text{ y = Cos\lparen2x\rparen}[/tex]
Therefore, the equation of the graph is y = Cos(2x).
The answer is CHOICE B : y = cos(2x)
