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anonymous

  • one year ago

Let (7,-5) be a point on the terminal side of theta. Find the exact values of sin, csc, and cot.

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  1. Nnesha
    • one year ago
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    (x,y) x = cos y= sin so in which quadrant you should draw the right triangle ?

  2. Nnesha
    • one year ago
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    |dw:1439523692837:dw|

  3. Nnesha
    • one year ago
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    remember that \[\huge\color{green}{\textrm CAST!}\] rule

  4. anonymous
    • one year ago
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    so I quadrant?

  5. Nnesha
    • one year ago
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    given point is (7,-5) what is cos and what is sin ?

  6. Nnesha
    • one year ago
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    like i said x-coordinate represents cos and y-coordinate = sin

  7. anonymous
    • one year ago
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    sin is -5 cos is 7?

  8. Nnesha
    • one year ago
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    yes right so in which quadrant sin is negative but cos is POSITIVE !

  9. anonymous
    • one year ago
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    so quadrant IV

  10. Nnesha
    • one year ago
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    yes right |dw:1439524044821:dw| apply the Pythagorean theorem to find 3rd side of right triangle

  11. Nnesha
    • one year ago
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    a^2+b^2=c^2 c=hypotenuse

  12. anonymous
    • one year ago
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    √74

  13. Nnesha
    • one year ago
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    right you need to know these definition of sin, cos , and tan \[\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }\] |dw:1439524382597:dw| so sin = ??

  14. anonymous
    • one year ago
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    so -5/√74

  15. Nnesha
    • one year ago
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    yes right but you can't leave the radical sign at the denominator so multiply denominator and numerator by sqrt{74}

  16. Nnesha
    • one year ago
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    \[\huge\rm \frac{ -5 }{ \sqrt{74} } \times \frac{ \sqrt{74} }{ \sqrt{74} }\]

  17. anonymous
    • one year ago
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    I think I did something wrong but I got -5

  18. Nnesha
    • one year ago
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    no that's not correct solve taht

  19. Nnesha
    • one year ago
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    \[\huge\rm \frac{ -5 }{ \sqrt{74} } \times \frac{ \sqrt{74} }{ \sqrt{74} }\] what did you get ?

  20. anonymous
    • one year ago
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    -.58?

  21. Nnesha
    • one year ago
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    well keep it in fraction form

  22. Nnesha
    • one year ago
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    *exact values*

  23. anonymous
    • one year ago
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    so -43.0/74?

  24. Nnesha
    • one year ago
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    \[\huge\rm \frac{ -5 }{ \sqrt{74} } \times \frac{ \sqrt{74} }{ \sqrt{74} }\] now we don't need decimal answer \[\frac{ -5\sqrt{74} }{ 74 }\]

  25. Nnesha
    • one year ago
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    ^^that is sin

  26. Nnesha
    • one year ago
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    now find csc remember sec, csc , cot are reciprocal of cos , sin , tan

  27. anonymous
    • one year ago
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    ohhh that looks so much better

  28. anonymous
    • one year ago
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    so csc is h/a?

  29. Nnesha
    • one year ago
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    sin and csc are reciprocal of each other if sin = o/h then csc = h/o

  30. anonymous
    • one year ago
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    oh opps so its √74/5

  31. Nnesha
    • one year ago
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    no

  32. Nnesha
    • one year ago
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    opposite side equal to what ?

  33. Nnesha
    • one year ago
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    |dw:1439525411597:dw| opposite of theta

  34. anonymous
    • one year ago
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    -5

  35. Nnesha
    • one year ago
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    yes so csc = ?

  36. anonymous
    • one year ago
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    oh did I just forget the -? √74/-5

  37. Nnesha
    • one year ago
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    yes right is not *just* :P

  38. anonymous
    • one year ago
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    haha sorry

  39. Nnesha
    • one year ago
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    okay \[\tan = \frac{ \sin }{ \cos } ~so ~\cot =\frac{ \cos }{ \sin }\]

  40. anonymous
    • one year ago
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    7/-5?

  41. Nnesha
    • one year ago
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    perfect!

  42. anonymous
    • one year ago
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    you are the best! thank you so much!

  43. Nnesha
    • one year ago
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    my pleasure.

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