Worked solution provided, but why is z = 360 deg rejected?

Feb 2010
8
0
Can any kind soul help me in the below?

Find z between 0 and 360 degrees which satisfy the equation.
1. sec^2 z = 4 sec z - 3

Answer:

sec^2 z = 4 sec z - 3
sec^2 z - 4 sec z + 3 = 0
(sec z - 3)( sec z - 1) = 0
sec z = 3 or sec z = 1
cos z = 1/3 or cos z = 1
z = 70.5 deg, z = 0, 360 deg(rejected)
cos is positive => so in 1st or 4th quadrant
z = 70.5, 360-70.5
= 70.5, 289.5

My question: why is z = 360 deg rejected?
why is z = 0 deg not rejected?
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
My question: why is z = 360 deg rejected?
why is z = 0 deg not rejected?
It is not clear why in this case, was your domain \(\displaystyle [0,360)\) or \(\displaystyle [0,360] \) ?
 
Feb 2010
8
0
Can any kind soul help me in the below?

Find z between 0 and 360 degrees which satisfy the equation.
1. sec^2 z = 4 sec z - 3

Answer:

sec^2 z = 4 sec z - 3
sec^2 z - 4 sec z + 3 = 0
(sec z - 3)( sec z - 1) = 0
sec z = 3 or sec z = 1
cos z = 1/3 or cos z = 1
z = 70.5 deg, z = 0, 360 deg(rejected)
cos is positive => so in 1st or 4th quadrant
z = 70.5, 360-70.5
= 70.5, 289.5

My question: why is z = 360 deg rejected?
why is z = 0 deg not rejected?
oh my, pickslides, you are really awesome!!