Question

Precalculus help please? I'm really confused on what to do. How do you solve for x?

sec (3x/2) = -2

Answer 1

start with
\[\cos(\frac{3x}{2})=-\frac{1}{2}\]
solve that for \(\frac{3x}{2}\) and then solve for \(x\)

Answer 2

cos (3x/2) = -1/2 = cos 2Pi/3 and cos 4Pi/4.
1). 3x/2 = 2Pi/3 -> x =.....
2). 3x/2 = 4Pi/3 -> x = ....

Answer 3

Oh, I'm doing the arccos(-1/2) wrong...I kind of forgot how to do it. Can you show me the steps please?

Answer 4

sec(3x/2) = -2. Since cos x =1/sec x, then
cos (3x/2) = -1/2 . Trig Conversion Table, or calculator give -1/2 = cos (2Pi/3) and = cos (4Pi/3). Theses 2 arcs have the same cos value (-1/2)
There are 2 solutions:
1. 3x/2 = 2Pi/3 -> x = ...
2. 3x/2 = 4Pi/3 -> x = ...