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anonymous

  • one year ago

what is the sin, cos, tan, csc, sec, and cot of 0 degrees?

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  1. jim_thompson5910
    • one year ago
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    Do you have a unit circle with you?

  2. anonymous
    • one year ago
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    yes

  3. jim_thompson5910
    • one year ago
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    ok locate the angle 0 degrees what is the corresponding point on the unit circle?

  4. anonymous
    • one year ago
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    1,0 ?

  5. jim_thompson5910
    • one year ago
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    use parenthesis but yeah, (1,0)

  6. jim_thompson5910
    • one year ago
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    the x coordinate is equal to cos(theta) the y coordinate is equal to sin(theta)

  7. jim_thompson5910
    • one year ago
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    so this means `cos(0) = 1` and `sin(0) = 0`

  8. anonymous
    • one year ago
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    tan(0)= 0?

  9. jim_thompson5910
    • one year ago
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    to compute `tan(0)` you use this trig identity \[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

  10. jim_thompson5910
    • one year ago
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    yeah you'll find that tan(0) = sin(0)/cos(0) = 0/1 = 0

  11. jim_thompson5910
    • one year ago
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    for the other three, use the identities listed on page 2 under the "Reciprocal Identities" section http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

  12. jim_thompson5910
    • one year ago
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    eg: csc(x) = 1/(sin(x))

  13. anonymous
    • one year ago
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    csc(0)= 0?

  14. jim_thompson5910
    • one year ago
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    what was sin(0) equal to again?

  15. anonymous
    • one year ago
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    0

  16. jim_thompson5910
    • one year ago
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    so csc(x) = 1/(sin(x)) csc(0) = 1/(sin(0)) csc(0) = 1/0 csc(0) = UND or NaN UND = undefined NaN = Not a Number

  17. jim_thompson5910
    • one year ago
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    1/0 is NOT the same as 0/1 0/1 = 0 1/0 is undefined because you can't have 0 in the denominator

  18. anonymous
    • one year ago
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    so i put undefined?

  19. jim_thompson5910
    • one year ago
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    yeah

  20. jim_thompson5910
    • one year ago
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    for csc(0)

  21. anonymous
    • one year ago
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    and for sec i also put undefined

  22. jim_thompson5910
    • one year ago
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    why? what was cos(0) ?

  23. anonymous
    • one year ago
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    1

  24. jim_thompson5910
    • one year ago
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    take the reciprocal of that to find sec(0)

  25. jim_thompson5910
    • one year ago
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    another way to view why csc(0) was undefined is that 0 doesn't have a reciprocal however, sec(0) is defined

  26. anonymous
    • one year ago
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    1?

  27. jim_thompson5910
    • one year ago
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    yeah sec(0) = 1

  28. anonymous
    • one year ago
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    cot(0)= undefined?

  29. jim_thompson5910
    • one year ago
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    why?

  30. anonymous
    • one year ago
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    tan(0)=0

  31. jim_thompson5910
    • one year ago
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    good, and taking the reciprocal of 0 leads to undefined

  32. jim_thompson5910
    • one year ago
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    so to summarize sin(0) = 0 cos(0) = 1 tan(0) = 0 csc(0) = und sec(0) = 1 cot(0) = und

  33. anonymous
    • one year ago
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    thanks.

  34. jim_thompson5910
    • one year ago
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    np

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