Question 122536
# 13


First a triangle with a leg of 8 and and a hypotenuse 17. Let x be the angle we'll refer to.
 

{{{drawing(500,500,-20,20,-20,20,
line(0,0,15,0),
line(15,0,15,8),
line(15,8,0,0),
locate(2.8,1.4,17),
locate(7.5,-1,x),
locate(15.2,4,8)
)}}}


 
By using pythagorean's theorem, we find that the other leg is 15 units



{{{drawing(500,500,-20,20,-20,20,
line(0,0,15,0),
line(15,0,15,8),
line(15,8,0,0),
locate(2.8,1.4,x),
locate(7.5,-1,15),
locate(15.2,4,8),
locate(7.5,6,17)
)}}}



Since {{{sin(x)=opposite/adjacent}}}  this means {{{x=arcsin(8/17)}}} (notice how the arcsine gives you an angle)

 

Now remember {{{cos(x)=adjacent/hypotenuse}}} and {{{sec(x)=1/cos(x)=hypotenuse/adjacent}}} (note: the secant and cosine functions are reciprocals of each other)
 


So {{{sec(x)=17/15}}}



which also means

 
{{{sec(arcsin(8/17))=17/15}}}


So the answer is C)