What is the amplitude, period and phase shift for y = 1/4 cos (3x +7)? Thank you, please show work.

Answer 1

rewrite it in the more general form as

y = (1/4) cos 3(x + 7/3)

compared to y = a cos k(Ø + p)

the amplitude is 1/4
the period is 2π/3
the phase shift is 7/3 to the left

for your equation in the original form a common mistake would be to state that the sphase shift is 7.
Note the step I took to avoid that error.