SOLUTION: derive the equation for the function with the following characteristics: 1. cot x: period 2 pi: phase shift p/4 to the left 2. csc x: period pi : phase shift pi/2 to the right

Question 805441: derive the equation for the function with the following characteristics:
1. cot x: period 2 pi: phase shift p/4 to the left
2. csc x: period pi : phase shift pi/2 to the right
3. tan x: period pi/2 : vertical shift 3 units up
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
derive the equation for the function with the following characteristics:
1. cot x: period 2 pi: phase shift p/4 to the left
Form: y = a*cot[b(x-c)]
Period = 2pi = pi/b; So b = 1/2
phase shift = c = p/4
Equation:
y = cot(1/2)(x - (p/4))
=================================
2. csc x: period pi : phase shift pi/2 to the right
Form: y = a*csc[b(x-c)]
Period = (2pi)/b = pi ; So b = 2
Phase shift = c = pi/2
Equation:
y = csc[2(x-(pi/2))
=========================
3. tan x: period pi/2 : vertical shift 3 units up
Form: y = a*tan[b(x-c)]+d
Period = pi/b = pi/2 ; So b = 2
Vertical shift = 3 = d
=======
Equation:
y = tan[2x] + 3
========================
Cheers,
Stan H.

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