Question

Solve the given equation
tan^2(theta)-2sec(theta)=2

Answer 1

@freckles I love you <3 just so you know xD
I've gotten to
sec(theta)=-1/2 and sec(theta)=1

Answer 2

But on the unit circle secant never = -1/2 and it equals 1 at 0

Answer 3

@peachpi :)?

Answer 4

Pi and -pi work, but they're certainly not the only answers. Positive and negative 1.231, 5.052, and 7.514 work as well.

Answer 5

how did you get those?

Answer 6

does pi(n) where n is an interger work?

Answer 7

tan² x -2 sec x = 2
sec² x - 1 -2 sec x = 2
sec²x - 2 sec x - 3 = 0
(sec x - 3)(sec x + 1) = 0
sec x = 3, sec x = -1

Answer 8

ooh crud. I added two instead of subtracting it

Answer 9

oh wow I messed up all over the place.

Answer 10

what did you do with the 2secx?

Answer 11

oh I see
2secx-sec^2x-2 = 0

Answer 12

I factored. and you have them reversed in the equation you just wrote

Answer 13

What's the correct way?

Answer 14

sec²x - 2 sec x - 3 = 0

Answer 15

ah right. so but secant never = 3 on the unit circle..

Answer 16

and = -1 and pi

Answer 17

yes, pi is a solution. For sec x = 3, the solution is x = arcsec 3

Answer 18

ah k. So for me with my little scientific calculator how do I do arc sec 3

Answer 19

sec = 1/cos
but with the inverse I want to be careful o.o

Answer 20

sec x = 3
cos x = 1/3
x = arccos (1/3)

Answer 21

oh! :)

Answer 22

that'll give you an angle in the 1st quadrant. Subtract it from 360 to get the angle in the 4th quadrant.

Answer 23

or rather 2pi

Answer 24

does it work to add two pi to that? or just subtracting it from 2pi?

Answer 25

the answers they give are
kpi = we have this one!
0.72+2kpi = we don't have this.
5.56+2kpi = and we dont' have this either.

Answer 26

adding 2pi just gives the same angle you already found. Subtracting x from 2pi gives the angle in the 4th quad.

Where did these answers come from?

Answer 27

aah I see
the answer part of the book
I'm doing the odd problems in my textbook which gives the answers in the back.

Answer 28

oh crap. Just a moment.

Answer 29

I'm getting 5.05 and 1.23

Answer 30

Sorry, yeah. I was looking at 7 instead of 5.
the answers are
(2k+1)pi, 1.23+2kpi, 5.05+2kpi

Answer 31

ok. you know how to get those?

Answer 32

um
1.23, 5.05 came from theta = arcos(1/3)
and pi came from sec(theta)=-1

Answer 33

and I understand the adding 2pi(k)

Answer 34

I'm not sure why the pi one is written as
(2k+1)pi ?

Answer 35

That's the same as π+2πk. They factored the pi out

Answer 36

ah ok I see.

Answer 37

haha I told myself I would keep doing these until I get the answer entirely on my own..but going like this it seems that won't be anytime soon =.=
K, this one makes sense now though :)

Answer 38

ok great. Maybe take a break if you don't have a deadline. These definitely take time to get used to

Answer 39

Final on Friday..hah but I may move onto studying another part.

Answer 40

ah.. I don't envy you. good luck

Answer 41

yeah xD thanks.

Answer 42

Precalc 2 man. phew.

Answer 43

For you it's probably no biggy xP

Answer 44

yeah give it a few years, you'll either never use it, or wonder how you lived without knowing it. There's no in-between

Answer 45

I fear it may be the latter D: Just because i despise it so much, i'm bound to end up being a math major lol

Answer 46

Welp, moving onto question next. Thanks for all your help :)