given tanθ= (-12)/35 and sinθ>0 find cosθ

Question

answer choices:

A cosθ = (-35)/37

B cosθ = (-12)/37

C cosθ = 12/37

D cosθ = 35/37

Answer 1

Sine is positive for any angle in quadrants I or II.

Tangent is negative in quadrants II or IV.  Therefore theta is in quadrant II.

using the Pythagorean theorem, the 'reference' triangle's hypotenuse measures 37.

Therefore sin θ = 12/37, cos θ = - 35/37.

Answer 2

since tan theta = (-12/35), we can set up a little right triangle using 12 and 35 as the lengths of the legs (remember that tan is opposite over adjacent)

 

 

 

            /|

          /  |

        /    |

      /      |  12 units

    /        |

  /          |

/ Θ         |

-----------

  35 units

 

 

hypotenuse = square root of (12² + 35²)

which equals 37

 

since the tan is negative, and we've been told that the sin is positive, that means cos must also be negative (let me know if you need an explanation here).  Cos is adjacent over hypotenuse, or 35/37, remember it must be negative so:

 

-35/37