Precalculus college

Question

2csc(2pi/4 x+25/4)

Find the period and the horizontal shift

Answer 1

2csc(2pix/4 + 25/4)

= 2csc[(2pi/4)(x +(25/4)/2pi/4))]

=2csc[(pi/2)(x + 25/2pi]

period = pi/b, b= pi/period

b = 2pi/period

period = 2pi/(pi/2) = 2pi(2/pi)= 4

phase shift = -25/2pi

general formula is

y = AcscB(x-C) + D

where A = amplitude

B = 2pi/period, period =2pi/B

C = phase shift= horizontal shift

D = midline = average y value= vertical shift

Answer 2

The function f(t)=a·csc(bx+c) has a phase shift of -c/b and a period of 2π/|b|:

Period: 2π/|b| = 2π/|2π/4| = 2π/(2π/4) = 4

Phase Shift: -c/b = -(-25/4)/(2π/4) = (25/4)/(2π/4) = 25/2π (to the left)

Hope this helped!

Answer 3

if written 2csc((π/2)(x-25/4)), then period is 2π/(π/2)=4 and offset is -25/4

if written 2csc((πx/2)-25/4), then period is 4 and offset is -25/(2π)

answers in units of x