What is the period and phase shift for f(x) = 3 tan(4x + π)?

Solution:

Given, f(x) = 3 tan(4x + π) --------------------- (1)

We have to find the period and phase shift.

The general equation is given by y = a tan(bx - c) + d ----------------- (2)

Where, a is the amplitude

f = b/π is the frequency

t = π/b is the period

θ = c/b is the phase shift

d is the vertical shift

On comparing (1) and (2),

a = 3

b = 4

c = -π

d = 0

Now, t = π/4

Therefore, the required period is π/4

Now, θ = (-π)/4

= -π/4

Therefore, the required phase shift is -π/4.

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What is the period and phase shift for f(x) = 3 tan(4x + π)?

Summary:

The period and phase shift for f(x) = 3 tan(4x + π) are π/4 and -π/4 respectively.