Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Hannah_Ahn

  • 2 years ago

solve algebraically for x: 4sin^2x=3tan^2-1 (answers: x=pi over 4, 3pi over 4, 5pi over 4, and 7pi over 4)

  • This Question is Closed
  1. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    is that tan^2 x?

  2. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes!

  3. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok this you can do, Just juggle about with identites first multiply both sides by cos ^2 x, LHS becomes 4sin^2 x cos ^2 x=(sin 2x)^2. Did you understand how?

  4. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Did you understand till here lets go step by step.

  5. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    shouldn't it be 2sin1/2^2

  6. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Do you know the identity 2sinx cosx=sin2x

  7. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep

  8. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2sin2^2*

  9. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    good so you have here 2sinx cos x the whole squared which is sin 2x the whole squared.

  10. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2sin2x^2**

  11. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So On the LHS there is sin ^2 2x which we can write it as 1- cos ^2 2x

  12. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    shouldn't it be 2sin^2 2x??

  13. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no do it agian 2 wont come.

  14. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4sin^2xcos^2 = 2sin2x^2 not sin2x^2 ?

  15. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no it is square in this one 2sinx cos x becomes sin 2x and another 2sinx cos x becomes sin 2x you need two 2's to make (sin x cosx)^2 (sin 2x)^2

  16. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OHHH!!!! I didn't know that .. :P thanks, let's keep it going

  17. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So yeah write sin ^2 2x as 1- cos ^2 2x. ok?

  18. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    kk

  19. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok so now come to RHS 3tan ^2 x * cos^2 x - cos ^2 x

  20. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    tan ^2 x *cos ^2 x=sin^2 x

  21. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so RHS becomes 3sin^2 x - cos^2 x

  22. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Now do you know the identities sin ^2 x=(1-cos2x)/2 and cos ^2 x=(1+cos 2x)/2

  23. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i don't know abhout the /2

  24. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin^2x = 1-cos^2x

  25. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no no that identity is \[\sin ^{2}x=(1-\cos 2x)/2\]

  26. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    over 2 ?

  27. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    isn't it pythagorean indentities

  28. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ITS \[\cos 2x \] not\[\cos ^{2}x\]

  29. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am so sorry. :S i didn't cover that identities yet

  30. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    those*

  31. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You have to use those identities you have 1- cos ^2 2x on the LHS so write everything in the RHS in terms of cos 2x

  32. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    even if you didn't know them now you know them... so substitue for sin ^2 x and cos ^2 x by using the identities i told you and tell me what you get...

  33. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    did you get what i'm trying to tell?

  34. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  35. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Good so tell me what do you have on the RHS...

  36. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    unfortunately, i cannot work it out with these identities that i didn't learn for a test. .

  37. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I'm sorry i don't know how to solve the problem in any other way.... Anyway if you want to continue with my method take LCM and all and simplify both sides you get cos ^2 2x=2cos 2x ths means cos 2x=0 and cos 2x=2(This case is not possible so the answer is just cos 2x=0

  38. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's okay I still appreciate you for what you've done. :)

  39. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay here's an alterative easier solution , You can use sec ^2 x= 1+tan ^2 x

  40. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So in the RHS write tan ^2 x as sec ^2 x -1 and simplify you get 8-4cos^2 x= 3sec^2 x. See if you understand till here....

  41. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Any doubts in what i have done? If not let us say cos^2 x is some t then obviously sec ^2 x=1/cos^2 x=1/t so you get 8-4t=3/t. 8t-4t^2=3. 4t^2-8t+3=0 this implies t=1/2 or t=3/2 t=3/2 is not possible hence t=1/2 or cos ^2 x=1/2 whose obvious solutions are pi/4,3pi/4 and so on.

  42. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lalaly wrong the equation when divided as by you becomes 4=3/cos^2x - cosec^2x

  43. lalaly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oops sorry

  44. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    did you get it hannah?

  45. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry i took a break . i am keep looking to figure out what you have done .

  46. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i feel like you are one of my tutor that i had in my past years :) haha he was great. anyway ..

  47. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    What a compliment \m/

  48. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Do you know how to solve quadratic equations?

  49. Hannah_Ahn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i learned it i will need to review it

  50. shankvee\
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Anyway read what i have done properly its not too hard to understand i've just substitued tan^2 x as sec ^2 x -1

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.