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hannahhaack

  • 6 months ago

Find the values of the six trigonometric functions of theta: cos θ = 35/37 constraint: tan θ < 0

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  1. hannahhaack
    • 6 months ago
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    |dw:1401422933563:dw|

  2. dan815
    • 6 months ago
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    six trignometric functions?

  3. hannahhaack
    • 6 months ago
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    yes. sin, tan, sec, cos, cot, csc

  4. dan815
    • 6 months ago
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    ok plug into calculator using the inverse buton

  5. hannahhaack
    • 6 months ago
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    to find all six? Can you baby it down for me haha

  6. dan815
    • 6 months ago
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    okay lol

  7. dan815
    • 6 months ago
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    so first look at your triangle its 35 in x and -37 in y

  8. dan815
    • 6 months ago
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    so enter 35/-37 in your calculator, and then do cos-1 (35/-37)

  9. dan815
    • 6 months ago
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    thats a button on your calculator cos inverse

  10. dan815
    • 6 months ago
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    do the same for sin and tan

  11. hannahhaack
    • 6 months ago
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    cos=2.811295299?

  12. dan815
    • 6 months ago
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    make sure you are using degree mode

  13. hannahhaack
    • 6 months ago
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    ok it is now cos=161.0753556

  14. dan815
    • 6 months ago
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    that answer is in radians which is fine too if your teacher wants that

  15. dan815
    • 6 months ago
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    alright thats one, now do the rest

  16. dan815
    • 6 months ago
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    remember that 1/sin= csc 1/cos=sec 1/tan=cot

  17. dan815
    • 6 months ago
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    by the way that is not the only solution,

  18. hannahhaack
    • 6 months ago
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    ya it usually accepts fractions.

  19. dan815
    • 6 months ago
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    |dw:1401423483117:dw|

  20. dan815
    • 6 months ago
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    it found that angle, but if your teacher is particular on you to only find tht last angle on the bottom

  21. hannahhaack
    • 6 months ago
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    So i just plugged in -37/\[\sqrt{2594}\]

  22. hannahhaack
    • 6 months ago
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    is it in quadrant 2 not 4?

  23. dan815
    • 6 months ago
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    i dont know its your choice what do you want??

  24. hannahhaack
    • 6 months ago
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    well the cos is positive and the tan is negative. so wont that be quad 4?

  25. dan815
    • 6 months ago
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    yeah

  26. hannahhaack
    • 6 months ago
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    ok now what would the hypotenus equal?

  27. dan815
    • 6 months ago
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    do Pythagorean thm

  28. dan815
    • 6 months ago
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    |dw:1401423730828:dw|

  29. dan815
    • 6 months ago
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    ok

  30. hannahhaack
    • 6 months ago
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    i get square root of 2594

  31. hannahhaack
    • 6 months ago
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    is that right? I might be doing my calcs wrong

  32. dan815
    • 6 months ago
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    looks about right

  33. myininaya
    • 6 months ago
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    |dw:1401423880441:dw|

  34. hannahhaack
    • 6 months ago
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    so would sin of theta=37/square root of 2594

  35. dan815
    • 6 months ago
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    the hypotenuse should be roughly sqrt2*36

  36. hannahhaack
    • 6 months ago
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    it says it is wrong

  37. hannahhaack
    • 6 months ago
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    square root of 36?

  38. dan815
    • 6 months ago
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    its -37

  39. dan815
    • 6 months ago
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    no nvm that, its just an approximation i dont have calc

  40. myininaya
    • 6 months ago
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    cos is adj/hyp you labeled the initial triangle a bit wrong

  41. dan815
    • 6 months ago
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    okay do it over

  42. hannahhaack
    • 6 months ago
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    can you show me the right triangle?

  43. dan815
    • 6 months ago
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    |dw:1401424044893:dw|

  44. myininaya
    • 6 months ago
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    good

  45. myininaya
    • 6 months ago
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    now find the opp measurement of the angle theta |dw:1401424168943:dw|

  46. hannahhaack
    • 6 months ago
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    and how did you get that?

  47. myininaya
    • 6 months ago
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    use the theorem we talked about last question

  48. myininaya
    • 6 months ago
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    you are given cos is 35/37

  49. hannahhaack
    • 6 months ago
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    right right right. got it

  50. hannahhaack
    • 6 months ago
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    none of those are negative?

  51. myininaya
    • 6 months ago
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    right cos is positive not negative

  52. myininaya
    • 6 months ago
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    sin is negative

  53. myininaya
    • 6 months ago
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    so you will definitely get a negative number for that opp measurement to theta

  54. hannahhaack
    • 6 months ago
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    i got 12

  55. myininaya
    • 6 months ago
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    and it should really be -12

  56. hannahhaack
    • 6 months ago
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    35^2+b^2=37^2

  57. hannahhaack
    • 6 months ago
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    b^2=144 b=12?

  58. myininaya
    • 6 months ago
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    or b=-12 we will go with b=-12 because we were given cos is + tan is - which makes sin -

  59. hannahhaack
    • 6 months ago
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    ok. so sin =-12/37

  60. myininaya
    • 6 months ago
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    |dw:1401424409906:dw| that symbolizes the triangle is to the right of zero but below 0 (that is talking about the signs)

  61. myininaya
    • 6 months ago
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    and yes

  62. hannahhaack
    • 6 months ago
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    that clarifies completely. what about this one? tan θ is undefined. constraint: π ≤ θ ≤ 2π

  63. hannahhaack
    • 6 months ago
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    find the six.

  64. dan815
    • 6 months ago
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    remember tan theta = sin theta/costheta so its undefin when cos theta= 0 which is at?

  65. hannahhaack
    • 6 months ago
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    so each one would be undefined?

  66. dan815
    • 6 months ago
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    no just the tan and the cot

  67. dan815
    • 6 months ago
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    well atually no cot is fine

  68. hannahhaack
    • 6 months ago
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    how do i find the rest?

  69. dan815
    • 6 months ago
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    have to first find this

  70. dan815
    • 6 months ago
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    tan theta= sin theta/cos theta => undefined when denominator =0 where cos theta =0

  71. dan815
    • 6 months ago
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    solve for cos theta = 0 , when theta is in that given interval pi to 2pi

  72. hannahhaack
    • 6 months ago
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    would it be 2pi/pi?

  73. dan815
    • 6 months ago
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    no

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