Question

solve 2sec^2(x/2) - 3sec(x/2) - 2 =0

Answer 1

So you have to solve 2sec^2(x/2) - 3sec(x/2) - 2 =0 for x, right?

Answer 2

findthe general solution

Answer 3

Well, for the moment, we can let y = sec^2(x/2) and if we did that, we would have

2y^2 - 3y - 2 = 0

Right?

Answer 4

And then factor? (2y+1)(y-2)

Answer 5

So after factoring we have
(2y + 1)(y - 2) = 0

And from here, we can set

2y + 1 = 0

and

y - 2 = 0

right?

Answer 6

Alright I got that part now, so i continued solving and ended up getting
sec(x/2) = -(.5) Which is no solution and and sec(x/2) = 2 which is where im now stuck

Answer 7

So you're left with

sec(x/2) = 2

From here, you can take the \(\sec^{-1}\) of both sides right?

Answer 8

I don't have a calculator to do that, have to look off a unit circle

Answer 9

How would you write the equation after taking the inverse secant of both sides?

Answer 10

idk what you mean but im at
cos(x/2) = pi/3 + 2pi and cos(x/2) = 5pi/3 +2pi
after switching to cos and looking at the unit circle

Answer 11

If you took the inverse secant of both sides, you would get

x/2 = \(\sec^{-1}(2)\) right?

Answer 12

yeah

Answer 13

Are you able to find \(\sec^{-1}(2)\)?

Answer 14

I think i got it thanks for taking me through the problem

Answer 15

Just to be sure, what did you get for your final result?

Answer 16

By the way, \(\sec^{-1}(x) \ne \cos(x)\)