8-1

5 sec theta +6=0
                  -6 = -6
5 sec theta= -6
/5                 /5
sec theta= -6/5= -33.557= -33degrees 32 mins. 25 sec.
-33.557+180=146.443= 146 degrees 26mins. 34 sec.
33.557+180=213.557= 213 degrees 32 mins 25 sec.

First you have to get sec theta by itself.  So you have to move all the other numbers to to the other side of the equation.  To do this, you have to subtract 6 on both sides.  Then you have 5 sec theta= -6.  Then you divide 5 on both sides and we have sec theta= -6/5.  Now, you have to find the decimal number of sec theta of -6/5.  When you plug that into your calculator, you get -33.557.  Next, you have to figure out what quadrants sec is negative in.  Cos is the recipracal thing of sec, so you know that cos is negative in quadrants two and three.  Now that you figured that out, in the second quadrant, you are supposed to make your number that you figured out negative and add 180 to it.  Doing this you get 146.443.  Then, you figure out what your number is in the third quadrant.  In the third quadrant, you make you number positive and add 180.  You get 213.557.  You cant keep any of your answers you found in decimals, so you have to convert them into degrees, minutes, and seconds.  To do this you just multipy the decimals by 60.