Find Amplitude, Period, and Phase Shift y=4csc(x-pi/2)

Problem

y=4*csc(x−π/2)

Solution

1. Identify the standard form of the cosecant function, which is y=a*csc(b*(x−h))+k In this equation, a=4 b=1 h=π/2 and k=0

2. Determine the amplitude. For the cosecant function, there is no amplitude in the traditional sense because the graph does not have a maximum or minimum value. However, the vertical stretch factor is |a|=4

3. Calculate the period using the formula P=(2*π)/|b| Since b=1 the period is 2*π

4. Identify the phase shift from the value of h Since the expression is (x−π/2) the phase shift is π/2 units to the right.

Final Answer

Amplitude: None (Vertical Stretch: 4)

Period: *2*π

Phase Shift: π/2

Want more problems? Check here!