91Ó°ÊÓ

The given function is $y=\sec \left(\mathrm{θ}\right)+2$.

A function of the form:

$y=a\sin b\left(\mathrm{θ}-h\right)+k,y=a\cos b\left(\mathrm{θ}-h\right)+k\text{and}y=a\tan b\left(\mathrm{θ}-h\right)+k$ has vertical shift $\left(k\right)$. And, a period of $\frac{360°}{\left|b\right|}\text{or}\frac{2\mathrm{π}}{\left|b\right|}$ for sine, cosecant, secant and cosine functions and a period of $\frac{180°}{\left|b\right|}\text{or}\frac{\mathrm{π}}{\left|b\right|}$ for tangent and cotangent function. The phase shift for the functions is $\left(h\right)$.

The amplitude of secant, cosecant, tangent and cotangent functions is not defined.

The equation for the midline is written as, $y=k$. A midline is a new reference line when the parent graph is stretched vertically up or down and then the graph oscillates about new reference line called the midline.

With the help of concept stated above, thevertical shift,equation of midline, amplitude and period of the function is evaluated as:

The vertical shift of $y=\sec \left(\mathrm{θ}\right)+2$is 2.

The equation of midline of $y=\sec \left(\mathrm{θ}\right)+2$is $y=2$.

The amplitude of $y=\sec \left(\mathrm{θ}\right)+2$is none.

The period of $y=\sec \left(\mathrm{θ}\right)+2$ is $\frac{2\mathrm{π}}{\left|1\right|}=2\mathrm{π}$.

The graph of the function $y=\sec \left(\mathrm{θ}\right)+2$ is shown below.

The vertical shift of $y=\sec \left(\mathrm{θ}\right)+2$is 2.

The equation of midline of $y=\sec \left(\mathrm{θ}\right)+2$ is $y=2$.

The amplitude of $y=\sec \left(\mathrm{θ}\right)+2$ is none.

The period of $y=\sec \left(\mathrm{θ}\right)+2$ is $\frac{2\mathrm{π}}{\left|1\right|}=2\mathrm{π}$.