How do you find the solution to 2-sectheta=5+sectheta if 0<=theta<360?

2 Answers
Dec 13, 2017

theta = 131.8

Explanation:

rearranging the terms we get
-2sectheta = 3 or 2sectheta = -3

sectheta = -3/2

Now we have to find for what value of theta < 360,
is the sec theta = -3/2

since we know sec & cos are reciprocal , we can state the above as
cos theta = -2/3

theta = arc cos(-2/3) = 131.8^@

Dec 13, 2017

131^@81; 228^@19

Explanation:

2 - sec t = 5 + sec t
- 2sec t = 3
sec t = -3/2
cos t = -2/3
Calculator and unit circle give 2 solutions:
t = +- 131^@81
We know the arc (- 131.81) is co-terminal to arc
(360 - 131.81 = 228.19)
Answers for (0, 360)
131^@81; 228^@19