Question

Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift.

a) ( y = 3 cosleft(x - pi/6right) - 4 )

b) ( y = 3 cosleft(x + pi/6right) - 4 )

c) ( y = 3 cosleft(x - pi/6right) + 4 )

d) ( y = 3 cosleft(x + pi/6right) + 4 )

Answer 1

The equation of the cosine function with the given amplitude, period, phase shift, and vertical shift is y = 3*cos(x - π/6) - 4.

Step-by-step explanation:

To write the equation of the cosine function with the given amplitude, period, phase shift, and vertical shift, we can use the form y = A*cos(B(x-C))+D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, option a) ( y = 3 cos(x - π/6) - 4 ) has an amplitude of 3, no vertical shift (D = 0), a phase shift of -π/6 (C = -π/6), and no change in frequency (B = 1).

Therefore, the correct equation is y = 3*cos(x - π/6) - 4.