Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

savac

Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. cos θ = − 5/9, sin θ > 0

  • one year ago
  • one year ago

  • This Question is Closed
  1. PeterPan
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay, let's make that drawing again, though following @hartnn 's advice, I'll do it properly this time ;) DRAW!!! |dw:1360757734426:dw|

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

    Cosine is adj/hyp, right?

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

    yes

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

    So, we have cosθ = -(5/9) We place the 5 and the 9, accordingly... |dw:1360757883210:dw| (Stop me when you don't understand)

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

    i understand

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

    Now, what's the length of this missing side... |dw:1360758005338:dw| (Hint: Pythagorean theorem)

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

    \[\sqrt{106}\] right?

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

    Remember, 9 is your hypotenuse When you have a^2 + b^2 = c^2 9 is your c :)

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

    \[\cos ^2(\theta)+\sin^2(\theta)=1\]

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

    \[\sin^2(\theta) = 1-\cos^2(\theta)\]

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

    \[\sqrt{56}\]

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

    \[\sin^2(\theta)=(\frac{- 5 }{ 9 })^2 -1\]

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

    i prefer the method provided by @PeterPan, because it shows you the inside out

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

    So, we can put sqrt(56) on here...|dw:1360758287438:dw| And you can easily get the other trig functions. Be careful though...

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

    @mathsmind You do need to do this to illustrate the pythagorean identities you posted. Though if you're not allowed to draw, better know the pythagorean (and other) identities by heart!!! :D

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

    yes that is what i said

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

    i said i prefer the other method to know the inside out

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

    we are allowed to draw on the test

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

    @savac REMEMBER THIS |dw:1360758381571:dw|

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

    although the identity was proven using pyth.

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

    whats that?

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

    ACTS!!!! |dw:1360758433801:dw|

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

    ohhhh thats smart

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

    savac PeterPan is doing a great job

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

    @mathsmind Thanks for the kudos! Much appreciated :)

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

    So back to this... |dw:1360758603756:dw| Can you now determine the rest of the trig functions of this theta?

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

    give me a mint

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

    min

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

    :D I was about to say something clever, but you beat me to it :)

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

    REMEMBER In this particular quadrant, only sine (and cosecant) are positive

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

    lol sorry running low on sleep

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

    ok i got sin=\[\sqrt{56}\]/9 tan=-\[\sqrt{56}\]/5 csc=9/\[\sqrt{56}\] sec=-9/5 cot=-5/\[\sqrt{56}\]

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

    What about cos?

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

    cos=-5/9

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

    And there you have it :)

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

    that was rright?

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

    Well yeah, unless you want to make it \[\huge \sqrt{56}=2\sqrt{14}\]

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

    wow i surprised myself. lol thank you very much

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

    Just place that right triangle in the correct quadrant, and you can't go wrong :) You'll notice that the horizontal bit was to the left of the x-axis, so strictly speaking, that's a -5, not a 5 :D

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

    thats what i thought it was

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

    actually since theta is in 2nd quadrant, that is its measure is between 90 to 180, the triangle will be , |dw:1360722028091:dw|

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

    Looks more complicated.

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

    but the way its solved and answers are correct.

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

    sin and cosec will be positive, all other ratios will be negative.

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

    Yay :)

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

    if you want to solve using diagram, then what i have drawn must be used . here, its solved using identities, which is altogether different method and doesn't need drawing triangle.

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

    Identities are harder to swallow, and they taste kinda awful too :(

    • one year ago
    • Attachments:

See more questions >>>

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.