anonymous
  • anonymous
Use a graphing calculator to solve the equation -3 cos t = 1 in the interval from
Mathematics
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
\[0\le \theta \le 2x\]
anonymous
  • anonymous
Round to the nearest hundredth and show your work.
freckles
  • freckles
is x suppose to be pi?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
oh yeah sorry it is
freckles
  • freckles
\[\cos(t)=\frac{-1}{3} \text{ on } 0 \le t \le 2\pi \\ \text{ one solution can be found just by taking } \arccos( ) \text{ of both sides } \\ \text{ other one we can find \it by using that } \\ \text{ cosine is even and has period } 2 \pi \\ \cos(-t)=\cos(t) \\ \text{ so we have } \\ \cos(-t+2\pi)=\frac{-1}{3} \\ \text{ take } \arccos( ) \text{ of both sides and solve for } t \]
anonymous
  • anonymous
@freckles can you keep going cuz i really dont know how to do this
anonymous
  • anonymous
I fanned you and gave you a medal
freckles
  • freckles
well were you not able to the first solution? it is just taking arccos( ) of both sides
freckles
  • freckles
\[\cos(t)=\frac{-1}{3} \text{ we could say one solution is } t=\arccos(\frac{-1}{3})\]
anonymous
  • anonymous
No im really confused, that's why i like when people go step by step
freckles
  • freckles
Oh I thought I gave you step by step
freckles
  • freckles
all I did there was take arccos( ) of both sides for that one solution
freckles
  • freckles
just as I said to do in the steps above
anonymous
  • anonymous
you did, but is that the answer?
freckles
  • freckles
that is one solution i also said how to find the other
freckles
  • freckles
use the fact that cos is even and has period 2pi
anonymous
  • anonymous
so the answer is -1/3?
freckles
  • freckles
how did you get that?
anonymous
  • anonymous
No i'm asking you, from your step by step that's what is above that everything is equalling -1/3
freckles
  • freckles
the equation is cos(t)=-1/3 we aren't solving for cos(t) if we were then we would done and the answer is -1/3 we are solving for t
freckles
  • freckles
one solution is given by taking arccos( ) of both sides of the equation cos(t)=-1/3
anonymous
  • anonymous
ok how do we do that?
freckles
  • freckles
one solution is given by t=arccos(-1/3)
freckles
  • freckles
and then the other solution is given by using the fact that cos is even and has period 2pi
anonymous
  • anonymous
t=4.37255207±2πn
freckles
  • freckles
let me give you an easy example to follow: \[\cos(\theta)=\frac{-1}{2} , \text{ where } 0 \le \theta \le 2 \pi \\ \text{ we know we are suppose to get solutions } \theta=\frac{2 \pi }{3} ,\frac{4\pi}{3} \\ \text{ we see we can get these solutions by doing : } \\ \text{ Answer one given by just takinng } \arccos( ) \text{ of both sides } \\ \theta=\arccos(\frac{-1}{2}) \\ \\ \text{ now the other solution comes from using the fact that } \\ \text{ cosine is even function and has period } 2\pi \\ \cos(-\theta+2\pi)=\frac{-1}{2} \\ \text{ solve for } \theta \text{ by first taking } \arccos( ) \text{ of both sides } \\ -\theta+2\pi=\arccos(\frac{-1}{2}) \\ \text{ now subtract } 2\pi \text{ on both sides } \\ -\theta=\arccos(\frac{-1}{2})-2\pi \\ \text{ last step multiply -1 on both sides } \\ \theta=-\arccos(\frac{-1}{2})+2\pi \\ \\ \text{ so the solutions to } \cos(\theta)=\frac{-1}{2} \text{ on } 0 \le \theta \le 2\pi \text{ are } \\ \theta=\arccos(\frac{-1}{2}) \text{ or } \theta=-\arccos(\frac{-1}{2})+2\pi \\ \text{ we can simplify these solutions } \\ \text{ We know } \arccos(\frac{-1}{2})=\frac{2\pi}{3} \\ \\\ \text{ so we have } \theta=\frac{2\pi}{3} \text{ or } \theta=-\frac{2\pi}{3}+2\pi=\frac{4\pi}{3} \\ \text{ just as we got way above just from using the unit circle }\]
freckles
  • freckles
|dw:1437253274947:dw|
freckles
  • freckles
anyways you can use the exact same process I used above
freckles
  • freckles
just take arccos() of both sides to get one solution
freckles
  • freckles
then rewrite the equation as cos(-t+2pi)=whatever where whatever is between -1 and 1 (inclusive) and take arccos( ) of both sides and then solve that resulting equation for t
freckles
  • freckles
\[\cos(t)=\frac{-1}{3} \\ \text{ one solution is } t=\arccos(\frac{-1}{3} ) \\ \text{ the other solution comes from solving } \cos(-t+2\pi)=\frac{-1}{3}\]
freckles
  • freckles
if I take arccos( ) of both sides of your second equation -t+2pi=arccos(-1/3) can you try to solve this for t?
freckles
  • freckles
it is just two steps
anonymous
  • anonymous
Is the answer theta 4/2pi?
freckles
  • freckles
do you know how to solve -x+4=6 for x?
anonymous
  • anonymous
yes
freckles
  • freckles
like you would subtract 4 on both sides -x=6-4 -x=2 and last step is multiply -1 on both sides x=-2 like this is the same type of equation here: \[-t+2\pi=\arccos(\frac{-1}{3} ) \\ \text{ subtract } 2\pi \text{ on both sides } \\ -t =\arccos(\frac{-1}{3})-2\pi \\ \text{ multiply -1 on both sides } \\ t=-\arccos(\frac{-1}{3})+2\pi\]
freckles
  • freckles
you have both solutions you can use your calculator to approximate them if you want
freckles
  • freckles
I think the instructions above do say to round to nearest hundredth so you will have to break out the calculator
anonymous
  • anonymous
Will you help me to the final answer?
freckles
  • freckles
I gave you both exact solutions... \[t=\arccos(\frac{-1}{3}) \\ t=-\arccos(\frac{-1}{3})+2\pi\] ?
freckles
  • freckles
oh are you saying you don't know how to plug it in the calculator?
freckles
  • freckles
there should be arcos typed on your calculator right above the cos button
freckles
  • freckles
arccos*
freckles
  • freckles
are it could be written as cos^(-1)
freckles
  • freckles
do you see it?
freckles
  • freckles
to access it on some calculators you have to press (shift or 2nd) can't remember which one
anonymous
  • anonymous
No i cant get a good answer it keeps saying error
anonymous
  • anonymous
t=8.19381854
freckles
  • freckles
what calculator do you use i can try to look it up and tell you what buttons to push
anonymous
  • anonymous
t=8.19381854
anonymous
  • anonymous
is that right?
freckles
  • freckles
oh i was waiting on you to tell me the calculator type but no
anonymous
  • anonymous
It's on a website cuz i dont have a calculator
freckles
  • freckles
arccos(-1/3)=1.91 by using a calculator so we already have that as a solution now replace the arccos(-1/3) in the other solution with 1.91 \[-1.91+2\pi\] you can do 3.14 as an approximation for pi 3.14*2=6.28 so what is -1.91+6.28
anonymous
  • anonymous
4.37
freckles
  • freckles
yes so remember you have two answers
anonymous
  • anonymous
So 4.37 is one, what's the other?
freckles
  • freckles
:(
anonymous
  • anonymous
what?
freckles
  • freckles
I just feel like you haven't listened to me \[t=\arccos(\frac{-1}{3}) \approx 1.91 \\ t=-\arccos(\frac{-1}{3})+2\pi \approx -1.91+2(3.14) =4.37\]
anonymous
  • anonymous
No I have, im just learning. Im sorry
freckles
  • freckles
ok well I hope you understood some of what I said
freckles
  • freckles
I have to leave now any questions before I go
anonymous
  • anonymous
Im gonna overview it right now, thank you very much for your help i appreciate it!

Looking for something else?

Not the answer you are looking for? Search for more explanations.