Express sin(-113 degree) as the function of a positive acute angle less than 45 degree

Question

jdoe0001 · Answer

on which quadrant do you think the angle $-113^o$ is at?

anonymous · Answer

3rd quadrant

jdoe0001 · Answer

ok, if you were to go counterclockwise, or 'positive' movement, where would the $113^o$ would be at? II quadrant, well, what you're after is its SUPPLEMENTARY angle

anonymous · Answer

67 degree ???

jdoe0001 · Answer

yes, $67^o$ on the II quadrant, where SINE is positive

jdoe0001 · Answer

and 67 is also acute

anonymous · Answer

but the answers are 
1) sin 57
2) cos 23
3) -cos 23
4) csc 23

jdoe0001 · Answer

ohh, it has to be less than 45, ok

anonymous · Answer

that's why i'm confusing :D

anonymous · Answer

do you have any idea?

jdoe0001 · Answer

no yet :|

anonymous · Answer

i typed in my calculator and i found that -cos23 is equal to sin(-113)

jdoe0001 · Answer

right, it has to be it's counterpart in the internal angles, cos(23)

jdoe0001 · Answer

the sin(60) = cos(30), becuase THE SAME line makes 60degrees from the origin, AND 30degrees from the arc, and those internal angles are usually a cos/sin relation

anonymous · Answer

|dw:1367708552997:dw|it looks like this right ?