A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Could somebody help me with the question: Find all the solutions for the equation: cosx = -1/2 Not looking for straight answers, but verification of the answer after an explanation on how to solve? Thank you!

  • This Question is Closed
  1. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you have a unit circle with you?

  2. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\bf cos(x)=\cfrac{1}{2}\implies cos^{-1}[cos(x)]=cos^{-1}\left( \cfrac{1}{2} \right)\implies x=cos^{-1}\left( \cfrac{1}{2} \right) \)

  3. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmm just notice is negative anyway \(\bf cos(x)=-\cfrac{1}{2}\implies cos^{-1}[cos(x)]=cos^{-1}\left( -\cfrac{1}{2} \right)\implies x=cos^{-1}\left( -\cfrac{1}{2} \right) \)

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The whole equation you replied with isn't showing up... @jdoe0001 But, I pulled up a unit circle.

  5. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    look at the points on the unit circle that have an x coordinate of -1/2 what are the angles that correspond to these points?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    240 degrees and 120 degrees? With the radian values being 4pi/3 and 2pi/3 respectively? @jim_thompson5910

  7. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    very good

  8. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    those are 2 of infinitely many angle values x that make cos(x) = -1/2 true

  9. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    add on 360 (in degree mode) or 2pi (radian mode) to get coterminal angles. You can also subtract 360 or 2pi to get other coterminal angles. There is no limit to how much you can add or subtract

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So if you're in degree mode, then the solution set is x = 120 + 360*n or x = 240 + 360*n where n is an integer

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So with the answer choices of: A. {2pi/3+npi | n = o. +/-1, +/-2, ... } B. {5pi/6+npi | n = o. +/-1, +/-2, ... } C. {5pi/6+2npi, 7pi/6+2npi | n = o. +/-1, +/-2, ... } D. {2pi/3+2npi , 4pi/3+2npi | n = o. +/-1, +/-2, ... } Would the answer be D? @jim_thompson5910

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes it is

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And could you help me with 1 more?

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sure

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, three actually. I think I got them correct, but just verifying. 1. For cos94cos37 + sin94sin37 (degrees) would the answer be cos57? 2. For sin8xcosx - cos8xsinx, I got (in terms of sin) sin9x 3. And for cos8xcos2x - sin8xsin2x, I got cos10x Just confused, on those, when to use (cos a + b), (cos a - b), (sin a + b), or (sin a - b)

  16. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    #1 is correct you can use a calculator to get cos(94)*cos(37)+sin(94)*sin(37) = 0.54463903501502 cos(57) = 0.54463903501502 both are equal to the same decimal value. You can also subtract the two values and you'll get 0 or very close to it

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    #2 is incorrect you use sin(A-B) = sin(A)cos(B) - cos(A)sin(B)

  18. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    #3 is correct cos(A-B) = cos(A)cos(B) + sin(A)sin(B)

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So for#2, instead of sin9x, would it be sin7x?

  20. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Can you explain when to use which identity? Like when to use the sin difference or sum, vs. the cos difference or sum? And when to use - vs +?

  22. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when you have the two 'cos' terms together, like with cos(A)cos(B) + sin(A)sin(B), you use the cos(A+B) or cos(A-B) identity

  23. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    whatever symbol is between the cos(A)cos(B) and sin(A)sin(B) is going to be the opposite inside the cosine on the left side

  24. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1436920932555:dw|

  25. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1436920967189:dw|

  26. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and if you have sin mixed with cosine, like sin(2x)cos(x) + cos(x)sin(2x), then you'll use sin(A+B) or sin(A-B)

  27. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1436921078884:dw|

  28. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It comes down to recognizing the form. That happens with lots of practice and memorization. You can look up the identities on a reference sheet like this one http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf (see the "Sum and Difference Formulas" section on page 2) but sometimes the teacher won't let you have a reference sheet like that. It all depends.

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.