The graph of a secant function y secbxc with a positive coe

The graph of a secant function, y = sec(bx+c), with a positive coefficient, b, is shown in the figure.

(a) Determine the value of b where b>0 . Decimal approximations will be marked incorrect.

b= ________

(b) Determine the value of c for the smallest positive value of c.  Decimal approximations will be marked incorrect.

Solution

period = 2pi /b =12

b=2pi/12

b=pi/6

phase shift =-c/b =3

c=-3b

c=-pi/2

y = sec((pi/6)x -(pi/2))

y = sec((pi/6)x -(pi/2) +2pi)

y = sec((pi/6)x +(3pi/2))

positive c=3pi/2