Question

1.HOW do you state the amplitude, period, phase shift and vertical shift for the function y= 2sin[4(angle symbol)-pie/2]-5?

2. Describe the function y= -5sin4 (angle symbol+30degrees)-4 as a transformation of the function y= sin(angle).

Answer 1

1. The amplitude is 2.
Since time does not appear in the equation, I cannot say what the period is.
The phase shift is pi/2
The vertical shift is -5

2. The function y= -5sin4 (angle symbol+30degrees)-4

has five times the amplitude of y= sin(angle).

It is also shifted vertically by -4, and has a phase shoft of -30 degrees.

Answer 2

Allow me to make a small correction to drwls solution.

in 1. the equation was given as
y= 2sin[4(angle symbol)-pie/2]-5

to read the phase shift directly from the equation the factor of 4 should be outside the bracket, so change it to

y= 2sin4[(angle symbol)-pie/8]-5

and now the phase shift is pi/8 to the right.

The period is 2pi/k for y = asink(theta)
so here the period is 2pi/4 or pi/2