Express sin 673 as a trig function of a positive acute angle less than 45? I don't understand how the answer is -cot43 HELP?

sin(673°)
= sin(360° + 313°)
= sin(313°)
= sin(180° + 133°)
= sin(133°)
= sin(90° + 43°)
= cos(43°)

This is actually nonsense, unless you indicate degrees!
(it will not be true with the implied radians.)

Next, it has to be cos, not cot.
673° = 720° - 47° ; and 720° is two complete turns, or periods of sine.
So sin 673° = sin (- 47°)
= - sin 47° (ASTC)
= - cos 43° (complementary function and angle)

Throw away multiples of 360 degrees.
673 - 720 = -47 degrees
That's between 0 and -90 degrees, where sine is negative and cos is positive.
sin -47 = cos(90 - 47) = cos 43
Correction invited!
Edit: fair comment, Keith.