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anonymous

  • one year ago

sin theta=-2/9 and tan theta is less than 0. Find sec theta and draw a reference angle. PLEASE HELP IM DYING I don't understand this

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  1. Nnesha
    • one year ago
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    |dw:1442457266673:dw| remember this CAST rule for signs

  2. prizzyjade
    • one year ago
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    Sin theta = -2/9 Tan theta<0 Sec theta = 1/cos theta Tan theta = sintheta/costheta Let tan = -1 -1(costheta)= -2/9 Costheta=2/9 Sectheta=1/(2/9) Sectheta= 9/2

  3. anonymous
    • one year ago
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    okay

  4. anonymous
    • one year ago
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    I'm still so confused haha

  5. Nnesha
    • one year ago
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    alright so given sin = -2/9 which is negative 2nd information given is tan < 0 so at which quadrant you should draw right triangle ?

  6. anonymous
    • one year ago
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    the second one right?

  7. Nnesha
    • one year ago
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    sin is positive at 2nd quadrant but the given sin is negative |dw:1442457589135:dw|

  8. anonymous
    • one year ago
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    OH I was confused which one was the second one, so would it be the fourth one then? the one in the bottom right-hand corner

  9. Nnesha
    • one year ago
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    |dw:1442457687986:dw|

  10. Nnesha
    • one year ago
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    in which quadrant sin is negative ?

  11. anonymous
    • one year ago
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    3 and 4 but tan is less than zero so I'm assuming that it would be quadrant 4

  12. Nnesha
    • one year ago
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    yes right |dw:1442457799099:dw|draw right triangle in 4th quadrant and remember this \[\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }\]

  13. Nnesha
    • one year ago
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    sin = opposite over hyp \[\huge\rm sin\theta=\frac{ opposite }{ hyp }=-\frac{ 2 }{ 9 }\]

  14. prizzyjade
    • one year ago
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    Tan must be in quadrant 4 since, sine is negative.and tangent is less 0 which means it is negative.

  15. Nnesha
    • one year ago
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    |dw:1442457929676:dw| remember adjacent and opposite sides depends on the angle

  16. anonymous
    • one year ago
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    right, so don't I use pythagorean theorem next?

  17. Nnesha
    • one year ago
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    yes right use pyth theorem to find 3rd side of right triangle

  18. anonymous
    • one year ago
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    ok, i got the square root of 77. now what?

  19. Nnesha
    • one year ago
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    |dw:1442458115705:dw| do you know the definition of sec ?

  20. Nnesha
    • one year ago
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    csc =1/sin sec = ??

  21. anonymous
    • one year ago
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    yeah it would be r/x right?

  22. Nnesha
    • one year ago
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    hm csc is reciprocal of 1/sin do you know what's reciprocal of sec ?

  23. anonymous
    • one year ago
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    huh? lol

  24. Nnesha
    • one year ago
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    \[\large\rm sin = \frac{ 1 }{ \csc }~~~~\cos=\frac{ 1 }{ \sec } ~~~~\tan=\frac{ 1 }{ \cot }\]

  25. Nnesha
    • one year ago
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    csc ,sec ,cot are reciprocal of sin ,cos ,tan

  26. anonymous
    • one year ago
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    ohhh ok so now what do i do?

  27. Nnesha
    • one year ago
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    to find sec you should know cos cos = adjacent over hyp so look at the triangle adjacent over hyp = ?

  28. anonymous
    • one year ago
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    so sec of theta would be 9 over square root 77?

  29. Nnesha
    • one year ago
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    yes right but you can't leave the radical at the denominator so multiply top and bottom with sqrt{77}\[\frac{ 9 }{ \sqrt{77}} \times \frac{ \sqrt{77} }{ \sqrt{77} }\]

  30. anonymous
    • one year ago
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    ohhh ok sooooo ok... that would be 1.025..?

  31. Nnesha
    • one year ago
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    hmm leave it as a fraction

  32. anonymous
    • one year ago
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    ummm,... lol ok in that case would it be 9 square root 7 over 77? I don't remember how to simplify those

  33. Nnesha
    • one year ago
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    just multiply the numerator by numerator and denominator by denominator do you mean sqrt{77} or just sqrt{7} ??

  34. anonymous
    • one year ago
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    sqrt(77) and yeah I know that haha, but I just don't know what that would come out to be

  35. Nnesha
    • one year ago
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    yes that's right

  36. anonymous
    • one year ago
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    oh great! so that's the answer?

  37. Nnesha
    • one year ago
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    yes i think so :=)

  38. anonymous
    • one year ago
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    Thank you so so much! would you mind helping me with one more question? It's tan theta = -7/24 and 90 degrees is less than 0 less than 180

  39. anonymous
    • one year ago
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    and find cos theta lol I just don't know how the 90 less than 0 less than 180 works in the problem

  40. Nnesha
    • one year ago
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    i've to go sorry one mint left :D

  41. anonymous
    • one year ago
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    oh lol well thanks anyway!

  42. Nnesha
    • one year ago
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    |dw:1442459319473:dw|

  43. Nnesha
    • one year ago
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    are you sure it's 90 less than 0 less than 180 ?

  44. anonymous
    • one year ago
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    oh my goodness thank you that is so helpful and yes

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