Question

Approximate, to nearest 10', the solutions of the equation in the interval [0 (degrees), 360 (Degrees))
12 tan^2t-5tant -2 = 0

Answer 1

@optiquest @zepdrix Sorry you guuuys

Answer 2

ooo crapper... i dont remember how to do `degree minutes seconds`.
Are you allowed to use a calculator on this?
I would assume so..

Answer 3

Yeah, so i just need the solutions and then i'm good to do the minute thing

Answer 4

oh ok cool

Answer 5

so factoring
tant(12tant-5)-2 = 0

Answer 6

no no no silly billy.

Answer 7

aw -.-

Answer 8

you have a quadratic equation.
how do we solve quadratics?

it either factors nicely,
or it doesn't (in which case we use our quadratic function to solve).

Answer 9

so how do I solve it?

Answer 10

your problem really looks like this:\[\Large\rm 12x^2-5x-2=0\]Where \(\Large\rm x=\tan t\)

Answer 11

Hmm won't factor nicely ;p
quadratic function time.

Answer 12

plug in all the bits and pieces, tell me what numbers you get

Answer 13

dangit...quad formula was a long time ago lol

Answer 14

do it -_- nao!

Answer 15

I doing eeet I doing eet

Answer 16

\[(-5\pm \sqrt{5^{2}-4(12)(2)})/2(12)(2)\]

Answer 17

right?

Answer 18

too many 2's in the bottom
and hold up, your c value is -2, not 2.

Answer 19

and it's -5 too right? :|

Answer 20

you gotta learn to use the equation tool sometime XD lol

Answer 21

oh yes, -5 as well

Answer 22

soo ( -5 (+/-) 11)/48

Answer 23

no, still too many 2's in the bottom

Answer 24

bottom is 2(a), yah?

Answer 25

i think you accidentally put 2(a)(c)

Answer 26

isn't it 2(a)(c)?

Answer 27

nooo :O

Answer 28

ooh...

Answer 29

so -5(+/-)11/24

Answer 30

yay good \c:/

Answer 31

Simplify it further to 2 values

Answer 32

hmm \[\huge\rm 12 x^2 - 5 x-2 =0\]
tan t = x
find two number if you multiply them you should get product of ac
and if you add or subtract them you should get middle term which is -5
heehe how about headphone method ??;3

Answer 33

Nooo, they're fractions >.< that sounds like a lot of work.
*grumble grumble*

Answer 34

<----

Answer 35

wait what?
the answers are 6/24, and -16/24 right?

Answer 36

oh take note that this time they want the answers within degrees

Answer 37

oh oh we made a mistake back here:
-5(+/-)11/24
should have been
5(+/-)11/24

Answer 38

oopsies

Answer 39

the first part is -(b)
plugging in your b gives you -(-5)

Answer 40

So i guess you get 16/24 and -6/24 ya?
simplify furtherrrrrrr -_-

Answer 41

0.66 and -0.25

Answer 42

So we have:\[\Large\rm x=\frac{2}{3},\qquad -\frac{1}{4}\]So,\[\Large\rm \tan t=\frac{2}{3},\qquad -\frac{1}{4}\]

Answer 43

To solve for t, we'll have to use our inverse function.

Answer 44

\[\Large\rm \tan t=\frac{2}{3}\]So,\[\Large\rm \tan^{-1}\left(\frac{2}{3}\right)=t\]

Answer 45

make sure you're in degree mode

Answer 46

33.690

Answer 47

good good good.
tangent is period in 180 degrees, so we get the same 2/3 if we add 180 degrees to our angle, ya?

Answer 48

So our first two solutions for our angle t are,
33.690 and 213.690

Answer 49

How bout the others?\[\Large\rm \tan^{-1}\left(-\frac{1}{4}\right)=t\]

Answer 50

hrm my calculator doesn't like that it says syntax error -.-

Answer 51

it doesn't like the negative in front of the 1/4
but is it - 14.036?

Answer 52

are you using the subtraction sign instead of the (-) button by mistake?

Answer 53

....meybee

Answer 54

yesss -14 degrees.
that doesn't lie in our interval though, right?
so we'll add 180 degrees to find the next one.

Answer 55

165.963

Answer 56

and 345.963

Answer 57

mmm ok good

Answer 58

i THINK we did these correctly.
i'm trying to see if i can check our work on a graph or something >.< sec

Answer 59

kks, ah, you always go the extra mile. :D

Answer 60

ehhh im not really sure on this one >.<
we'll just go with this, it's probably right.

you understand how to convert your angles to degrees, minutes, seconds from that point?

Answer 61

oh shooo i forgot to do that haha THANK YOU

Answer 62

yay team \c:/

Answer 63

yayaa