A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Use a graphing calculator to solve the equation 3 cos t = 1 in the interval from
anonymous
 one year ago
Use a graphing calculator to solve the equation 3 cos t = 1 in the interval from

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[0\le \theta \le 2x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Round to the nearest hundredth and show your work.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1is x suppose to be pi?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\cos(t)=\frac{1}{3} \text{ on } 0 \le t \le 2\pi \\ \text{ one solution can be found just by taking } \arccos( ) \text{ of both sides } \\ \text{ other one we can find \it by using that } \\ \text{ cosine is even and has period } 2 \pi \\ \cos(t)=\cos(t) \\ \text{ so we have } \\ \cos(t+2\pi)=\frac{1}{3} \\ \text{ take } \arccos( ) \text{ of both sides and solve for } t \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles can you keep going cuz i really dont know how to do this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I fanned you and gave you a medal

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well were you not able to the first solution? it is just taking arccos( ) of both sides

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\cos(t)=\frac{1}{3} \text{ we could say one solution is } t=\arccos(\frac{1}{3})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No im really confused, that's why i like when people go step by step

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Oh I thought I gave you step by step

freckles
 one year ago
Best ResponseYou've already chosen the best response.1all I did there was take arccos( ) of both sides for that one solution

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just as I said to do in the steps above

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you did, but is that the answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that is one solution i also said how to find the other

freckles
 one year ago
Best ResponseYou've already chosen the best response.1use the fact that cos is even and has period 2pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer is 1/3?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1how did you get that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No i'm asking you, from your step by step that's what is above that everything is equalling 1/3

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the 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
 one year ago
Best ResponseYou've already chosen the best response.1one solution is given by taking arccos( ) of both sides of the equation cos(t)=1/3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok how do we do that?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1one solution is given by t=arccos(1/3)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and then the other solution is given by using the fact that cos is even and has period 2pi

freckles
 one year ago
Best ResponseYou've already chosen the best response.1let 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437253274947:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1anyways you can use the exact same process I used above

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just take arccos() of both sides to get one solution

freckles
 one year ago
Best ResponseYou've already chosen the best response.1then 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
 one year ago
Best ResponseYou've already chosen the best response.1\[\cos(t)=\frac{1}{3} \\ \text{ one solution is } t=\arccos(\frac{1}{3} ) \\ \text{ the other solution comes from solving } \cos(t+2\pi)=\frac{1}{3}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if I take arccos( ) of both sides of your second equation t+2pi=arccos(1/3) can you try to solve this for t?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is the answer theta 4/2pi?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to solve x+4=6 for x?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1like you would subtract 4 on both sides x=64 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
 one year ago
Best ResponseYou've already chosen the best response.1you have both solutions you can use your calculator to approximate them if you want

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I think the instructions above do say to round to nearest hundredth so you will have to break out the calculator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Will you help me to the final answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I gave you both exact solutions... \[t=\arccos(\frac{1}{3}) \\ t=\arccos(\frac{1}{3})+2\pi\] ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oh are you saying you don't know how to plug it in the calculator?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1there should be arcos typed on your calculator right above the cos button

freckles
 one year ago
Best ResponseYou've already chosen the best response.1are it could be written as cos^(1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1to access it on some calculators you have to press (shift or 2nd) can't remember which one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No i cant get a good answer it keeps saying error

freckles
 one year ago
Best ResponseYou've already chosen the best response.1what calculator do you use i can try to look it up and tell you what buttons to push

freckles
 one year ago
Best ResponseYou've already chosen the best response.1oh i was waiting on you to tell me the calculator type but no

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's on a website cuz i dont have a calculator

freckles
 one year ago
Best ResponseYou've already chosen the best response.1arccos(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

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes so remember you have two answers

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 4.37 is one, what's the other?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I 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
 one year ago
Best ResponseYou've already chosen the best response.0No I have, im just learning. Im sorry

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok well I hope you understood some of what I said

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I have to leave now any questions before I go

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im gonna overview it right now, thank you very much for your help i appreciate it!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.