Find the period (in radians), the phase shift (in radians) and the vertical shift of the graph of the function below.
y=3 sec (ѳ/2- (3π)/4)
The general form for the function y = a sec(b(θ - c)) is y = a sec(b(θ - c)) + d.
Comparing this general form to the given function y = 3 sec(θ/2 - (3π)/4), we can see that:
a = 3
b = 1/2
c = 3π/4
d = 0
The period of y = a sec(bθ) is 2π/b. Therefore, the period of the given function y = 3 sec(θ/2) is 2π/(1/2) = 4π.
The phase shift of y = a sec(b(θ - c)) is c. Therefore, the phase shift of the given function y = 3 sec(θ/2 - (3π)/4) is (3π)/4.
The vertical shift of y = a sec(bθ) is 0. Therefore, the vertical shift of the given function y = 3 sec(θ/2 - (3π)/4) is 0.
So, the period is 4π radians, the phase shift is (3π)/4 radians, and the vertical shift is 0.