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@freckles I love you <3 just so you know xD I've gotten to sec(theta)=-1/2 and sec(theta)=1
But on the unit circle secant never = -1/2 and it equals 1 at 0
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.
how did you get those?
does pi(n) where n is an interger work?
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
ooh crud. I added two instead of subtracting it
oh wow I messed up all over the place.
what did you do with the 2secx?
oh I see 2secx-sec^2x-2 = 0
I factored. and you have them reversed in the equation you just wrote
What's the correct way?
sec²x - 2 sec x - 3 = 0
ah right. so but secant never = 3 on the unit circle..
and = -1 and pi
yes, pi is a solution. For sec x = 3, the solution is x = arcsec 3
ah k. So for me with my little scientific calculator how do I do arc sec 3
sec = 1/cos but with the inverse I want to be careful o.o
sec x = 3 cos x = 1/3 x = arccos (1/3)
that'll give you an angle in the 1st quadrant. Subtract it from 360 to get the angle in the 4th quadrant.
or rather 2pi
does it work to add two pi to that? or just subtracting it from 2pi?
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.
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?
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.
oh crap. Just a moment.
I'm getting 5.05 and 1.23
Sorry, yeah. I was looking at 7 instead of 5. the answers are (2k+1)pi, 1.23+2kpi, 5.05+2kpi
ok. you know how to get those?
um 1.23, 5.05 came from theta = arcos(1/3) and pi came from sec(theta)=-1
and I understand the adding 2pi(k)
I'm not sure why the pi one is written as (2k+1)pi ?
That's the same as π+2πk. They factored the pi out
ah ok I see.
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 :)
ok great. Maybe take a break if you don't have a deadline. These definitely take time to get used to
Final on Friday..hah but I may move onto studying another part.
ah.. I don't envy you. good luck
yeah xD thanks.
Precalc 2 man. phew.
For you it's probably no biggy xP
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
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
Welp, moving onto question next. Thanks for all your help :)