Answer:
y = - cos ( [tex]\frac{3}{4}[/tex] x + [tex]\frac{\pi }{4}[/tex] )
Step-by-step explanation:
y = A cos ( Bx + C) + D
Vertical shift D = 0
A = - 1
Compression / Stretching B
Period of given function is [tex]\frac{8\pi }{3}[/tex]
Period of cos x is 2π
[tex]\frac{8\pi }{3}[/tex] = [tex]\frac{2\pi }{B}[/tex] ⇒ B = [tex]\frac{3}{4}[/tex]
Horizontal shift is C ÷ B
Horizontal shift of given function is [tex]\frac{\pi }{3}[/tex]
[tex]\frac{\pi }{3}[/tex] = C ÷ [tex]\frac{3}{4}[/tex] ⇒ C = [tex]\frac{\pi }{4}[/tex]
So, the equation of given function is
y = - cos ( [tex]\frac{3}{4}[/tex] x + [tex]\frac{\pi }{4}[/tex] )
