<PRE><B>Question 773389</B>

{{{tan( theta) =Y/X}}}

he value of theta for the ordered pair ({{{-3}}},{{{ 5}}})

{{{tan( theta) =5/-3}}}

{{{tan( theta) =-5/3}}}

{{{ theta =-59.04}}}°

if {{{tan ( theta) = -5/3}}}, then the terminal side of ( theta) (the angle) lies  in quadrant {{{II}}}

recall:

 Quadrant {{{I}}} is 0°-90°, 
Quadrant {{{II}}} is 90°-180°, 
Quadrant {{{III}}} is 180°-270°, and 
Quadrant {{{IV}}} is 270°-360°

0 -90 degrees  is the {{{positive}}} x-axis and the {{{positive}}} y-axis
90-180 degrees is the {{{negative}}} x-axis and the {{{positive}}} y-axis
 180- 270 degrees is the {{{negative}}} x-axis and the {{{negative}}} y-axis
360 degrees, of course, is full circle and again the {{{positive}}} x-axis (like 0 degrees) and the {{{negative}}} y-axis

since given ({{{-3}}},{{{ 5}}}), you know that {{{x}}} is negative and {{{y}}}, your answer is Quadrant {{{II}}}

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