Find sec(t)

Question

The point (5,-6) is on the terminal side of angle t. Find sec(t).

Answer 1

 

The point (5, -6) is in quadrant IV, where x is positive and y is negative.

 

 

     1   2    3   4   5          

 •_______________

    •   t°            |_|   

-1     •                 |

-2         •             |

-3             •         |

-4                 •     |

-5                     • | (5, -6)

-6                        •

 

 

We are looking for the secant of reference angle t.

secant is the reciprocal of cosine,

cosine = adjacent / hypotenuse, so secant = hypotenuse / adjacent

 

We use the pythagorean theorem to find the hypotenuse.

 

     c² = a² + b²

         = 5² + (-6)²

         = 25 + 36

         = 61

      c = √61

 

The hypotenuse is √61

 

The adjacent side to angle t has length of 5.

The hypotenuse has length of √61

 

sec t = hypotenuse / adjacent

 

sex t = √61/5