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★ Analytical Trigonometry ★

Let it's general format be -
[tex]f(x) = a \: cos \: b(x - c) + d \\ [/tex]
Having frequency as -
[tex]f = \frac{b}{2\pi} [/tex]
According to provided data -

amplitude : 3
Hence , a = 3

[tex]frequency = \frac{1}{2\pi} [/tex]
Hence b = 1

Phase Shift to the left of 2 : c = -2 [ left to the y-axis ]

Midline of y = 4

Hence d = 4

Now finally substituting every value obtained -

The equation of Cos function is -

[tex]y = 3cos1(x - 2) + 4[/tex]

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