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JayDelV

  • one year ago

If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ?

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  1. Nnesha
    • one year ago
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    |dw:1439502598438:dw| at which quadrant sin is positive

  2. JayDelV
    • one year ago
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    First

  3. Nnesha
    • one year ago
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    remember that CAST rule for signs

  4. Nnesha
    • one year ago
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    yes first and ?

  5. JayDelV
    • one year ago
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    Oh and second

  6. Nnesha
    • one year ago
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    yes right sin positive in 1st and 2nd quadrant given is tan < 0 is is less than 0 so at which quadrant you should draw a right triangle ?

  7. JayDelV
    • one year ago
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    second?

  8. Nnesha
    • one year ago
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    yes right tan is negative in 2nd quadrant <0 |dw:1439502785727:dw| draw a right triangle \[\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }\]

  9. Nnesha
    • one year ago
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    sin = opposite over hyp so \[\huge\rm \sin \theta = \frac{ 3 }{ 7 }=\frac{ opposite }{ hyp }\] opposite =3 hyp = 7 |dw:1439502881389:dw|

  10. Nnesha
    • one year ago
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    now apply the Pythagorean theorem to find 3rd side of right triangle

  11. Nnesha
    • one year ago
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    \[\huge\rm a^2+b^2=c^2\] c=hypotenuse

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