Question 1159744

The terminal side of angle {{{theta}}}, in standard position, lies in the {{{fourth}}} quadrant, and 

{{{cos(theta)=5/13}}}  



in this specific right-angled triangle the adjacent side={{{5}}} and the hypotenuse ={{{13}}}

opposite side is {{{sqrt(13^2-5^2)=sqrt(144)=12}}}

in the {{{fourth }}}quadrant {{{sin(theta)}}}  is negative, we use {{{-12}}}


{{{sin(theta) =-12/13}}}


{{{tan(theta) =opposite /adjacent}}}


{{{tan(theta) =-12/5}}}