How do you find the solution to 2-sectheta=5+sectheta2secθ=5+secθ if 0<=theta<3600θ<360?

2 Answers
Dec 13, 2017

theta = 131.8θ=131.8

Explanation:

rearranging the terms we get
-2sectheta = 32secθ=3 or 2sectheta = -32secθ=3

sectheta = -3/2secθ=32

Now we have to find for what value of theta < 360θ<360,
is the sec theta = -3/2secθ=32

since we know sec & cossec&cos are reciprocal , we can state the above as
cos theta = -2/3cosθ=23

theta = arc cos(-2/3)θ=arccos(23) = 131.8^@131.8

Dec 13, 2017

131^@81; 228^@1913181;22819

Explanation:

2 - sec t = 5 + sec t
- 2sec t = 3
sec t = -3/2sect=32
cos t = -2/3cost=23
Calculator and unit circle give 2 solutions:
t = +- 131^@81t=±13181
We know the arc (- 131.81) is co-terminal to arc
(360 - 131.81 = 228.19)
Answers for (0, 360)
131^@81; 228^@1913181;22819