y = sec(2θ + π), Determine amplitude, period, midline, phase shift?

The period is pi (because the angular frequency is 2).

The midline is the x axis.

The phase shift is usually found by putting the operand of the trig function into the form w(theta - phi), so in your case, the "2 theta + pi" would become 2(theta - (-pi/2)), and it would be appropriate to say that the phase shift is -pi/2.

"Amplitude" is a word more frequently applied to sine and cosine functions only, but if it must be applied to a secant, the amplitude of this particular function would be 1, since there is no coefficient multiplying the secant.

Y = sec(2*@) + Pi)

Template:

Y = sec(w*@ + phase shift)

Amplitude;

sec(x) = 1/cos(x)

|sec(2*@)| = 1 to inf over -(Pi/4) to +(Pi/4)

Period;

w = 2

2*Pi*f = 2

Pi*f = `

Pi/T = 1

T = Pi

midline;

y axis

phase shift;

Pi