Write equations for each of the following: A secant function with period 3π/2, vertical translation up 1, and phase shift π/3

Answer 1

Secant and Cosine have almost the same properties because they are reciprocals.

y= a sec (b(x-c)) + d

Where:

|a| = amplitude

2π / b = period

c = phase shift

d = vertical translation.

(1) Didn't say anything about amplitude. I assume it's 1 (a=1).

(2) To find the period:

2π / b = 3π / 2 then solve for b.

2•2π /3π = b

b = 4/3

Then the equation with c = π/3 and d=1 is:

y= sec [(4/3)(x-π/3)] + 1