<PRE><B>Question 180736</B>
Concepts:
cosB=x/r
sinB=y/r
tanB=y/x
secB=r/x
cscB=r/y
cotB=x/y

x^2 + y^2 = r^2

Since cosB=4/5  then x=4 and r=5

(4)^2 + y^2 = (5)^2
16 + y^2 =25
y^2 = 9
y = 3 or y=-3

***************
sinB= 3/5 or -3/5
tanB=3/4 or -3/4
secB=5/4
cscB=5/3 or -5/3
cotB= 4/3 or -4/3


****************JUST REALIZE I PROVIDED YOU WITH PRINCIPAL RATIOS AND QUESTION IS ASKING FOR PRINCIPAL ANGLES******
B= cos^-1(4/5)=36.87 degrees
Note that cos is also positive in quadrant IV....so you can have another angle in standard position
360-36.87=323.13</PRE>