Math Help - Find Value of Trig. Expression

1. Find Value of Trig. Expression

Hi,
the directions are: find the exact value of the expression. Use a graphing utility to verify your results.

I've done the problem but I'm not sure if I've done it right... and I'm also unsure about the negative in the original equation:

the problem is::

sec[arctan(-3/5)]

this is what I've done so far-
I drew the triangle using tan=opposite/adjacent

then I used pythagorean theorem to find the hypotenuse. it was the square root of (34).

after this I found the sec. which was the square root of (34)/5

my question is if what I've is correct and where does the negative sign go in finding the solution?

thank you!!

p.s - I don't know how to make the square roots appear on the screen... that's why I wrote it out... everything in parentheses is under the square root.

2. Hello, overduex!

Find the exact value of: . $\sec\left[\arctan\left(-\frac{3}{5}\right)\right]$

You're thinking is correct . . . up to a point.

Let $\theta \,=\,\arctan\left(-\frac{3}{5}\right)\quad\Rightarrow\quad\tan\theta \:=\:-\frac{3}{5}$

Tangent is negative in Quadrants 2 and 4.

There are two possible positions for angle $\theta.$
Code:
                      |
*           |
:  *  √34   |
3:     *     |
:        *  |      5
- - + - - - - - + - - - - - + - -
-5     |  *        :
|     *     :-3
|  √34   *  :
|           *
|

Hence, there are two possible values for the secant.

. . $\sec\theta \;=\;\pm\frac{\sqrt{34}}{5}$

3. Wow. Thanks!
I had completely forgotten about the possibility of there being two positions for the angle.
Thank you so much!!!