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anonymous

  • one year ago

how does csc(-120) equal to -csc(120)?

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  1. Nnesha
    • one year ago
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    sin and tan are odd cos = even \[\large\rm sin(-\theta)= -\sin \theta\]\[\large\rm cos(-\theta)= \cos \theta\]\[\large\rm Tan(-\theta)= - Tan \theta\]

  2. anonymous
    • one year ago
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    I still don't understand

  3. Nnesha
    • one year ago
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    what is reciprocal of sin ,cos and tan ???

  4. anonymous
    • one year ago
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    Honestly I have no idea. I am the worst with trigonometry. I don't understand it whatsoever

  5. Nnesha
    • one year ago
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    then u need to start it over \[\large\rm sin =\frac{ 1 }{ \csc }~~\cos=\frac{ 1 }{ \sec }~~~\tan=\frac{ 1 }{ \cot }=(\frac{ \sin }{ \cos })\] reciprocal of sin is 1/csc reciprocal of cos is 1/sec reciprocal of tan is 1/cost or you can say sin /cos csc=1/sin sec=1/cos cot=1/tan csc , sec and cot are reciprocal of sin , cos and tan

  6. Nnesha
    • one year ago
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    if sin =a/b then csc = b/a

  7. Nnesha
    • one year ago
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    so if sin is odd function then csc is odd or even ?

  8. anonymous
    • one year ago
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    odd

  9. Nnesha
    • one year ago
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    yes right that's how \[\huge\rm csc(-120)= - \csc(120)\]

  10. dumbcow
    • one year ago
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    another way of looking at it is using the unit circle and fact that neg angle goes clock-wise |dw:1440006652430:dw|

  11. anonymous
    • one year ago
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    but I'm just not understanding how the negative comes out

  12. dumbcow
    • one year ago
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    sin refers to "y-value" , on the circle sin(-120) is the neg y-value of sin(120)

  13. dumbcow
    • one year ago
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    |dw:1440007033356:dw|

  14. anonymous
    • one year ago
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    oooooh okay, i get it more now lol. thank you!

  15. anonymous
    • one year ago
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    is this also true for cosine ?

  16. Nnesha
    • one year ago
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    cos = odd

  17. Nnesha
    • one year ago
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    \[\large\rm cos (-45)= \cos(45)\] |dw:1440007938868:dw| x-coordinate represents cos function

  18. anonymous
    • one year ago
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    wouldn't the cosine be negative too since it's in the 3rd quadrant ?

  19. Nnesha
    • one year ago
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    yeah i was just thinking about this .. cos is also negative in 2nd quadrant

  20. Nnesha
    • one year ago
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    for odd and oven just remember sin(-x)= -sin(x) cos(-x)=cos(x) tan(-x)= -tan(x)

  21. Nnesha
    • one year ago
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    @dumbcow

  22. anonymous
    • one year ago
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    so it's not true for cos of theta ?

  23. Nnesha
    • one year ago
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    yes right cos (-120) = cos(120)

  24. Nnesha
    • one year ago
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    cos is even

  25. anonymous
    • one year ago
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    how do I prove that ?

  26. anonymous
    • one year ago
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    my question says to pick a value of theta and to test the theory

  27. Nnesha
    • one year ago
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    i guess because cos is negative in 2nd quadrant and in 3rd quadrant so negative times negative = positive even

  28. Nnesha
    • one year ago
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    :P i just know the basic stuff don't know how to explain better than that sorry

  29. anonymous
    • one year ago
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    thank you

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