Answer:
[tex]y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)[/tex]
Step-by-step explanation:
Given
[tex]Amplitude = \frac{\pi}{2}[/tex]
[tex]Period = 3[/tex]
Required
Write the equivalent cosine function
The general formula is:
[tex]y = acos(bx)[/tex]
Where
[tex]amplitude = |a|[/tex]
[tex]period = \frac{2\pi}{b}[/tex]
Substitute [tex]\frac{\pi}{2}[/tex] for amplitude in [tex]amplitude = |a|[/tex]
[tex]|a| = \frac{\pi}{2}[/tex]
[tex]a = \frac{\pi}{2}[/tex]
Substitute 3 for period in [tex]period = \frac{2\pi}{b}[/tex]
[tex]\frac{2\pi}{b} = 3[/tex]
Multiply both sides by b
[tex]2\pi = 3b[/tex]
Divide through by 3
[tex]b = \frac{2\pi}{3}[/tex]
Hence;
[tex]y = acos(bx)[/tex] becomes
[tex]y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)[/tex]
