#### (a)

The graph of $y=csc x$ has vertical asymptotes at $0, pmpi,pm2pi,. . .$

$t_{n}=npi, nin I$

#### (b)

$y=csc x$ has no maximum value.

#### (c)

$y=csc x$ has no minimum value.

#### (a)

The graph of $y=sec x$ has vertical asymptotes at $pmdfrac{pi}{2}, pmdfrac{3pi}{2}$,. . .

$t_{n}=dfrac{pi}{2}+npi, nin I$

#### (b)

$y=sec x$ has no maximum value.

#### (c)

$y=sec x$ has no minimum value.

#### (a)

The graph of $y=cot x$ has vertical asymptotes at $0,pmpi,pm2pi,. . .$

$$
t_{n}=npi, nin I
$$

#### (b)

The graph of $y=cot x$ intersects the $x$-axis at $pmdfrac{pi}{2}$,$pmdfrac{3pi}{2}, . . .$

$t_{n}=dfrac{pi}{2}+npi$, $nin I$

The values of $x$ for which $y=csc x$ and $y=sec x$, $textbf{intersect}$ are

$x=-5.5, -2.35, 0.79, 3.93$, the same values for which $y=sin x$ and $y=cos x$ were determined to intersect in Lesson $6.3$.

$x=-5.5, -2.35, 0.79, 3.93$

Yes; the graphs of $y=cscleft(x+dfrac{pi}{2} right)$ and $y=sec x$ are identical.

Answers may vary.For example, reflect the graph of $y=tan x$ across the $y$-axis and then translate the graph $dfrac{pi}{2}$ units to the left.

#### (a)

period$=2pi$

#### (b)

period$=pi$

#### (c)

period$=2pi$

#### (d)

period$=4pi$