I'm confused about how to do the question in it's entirety.

Question

Find  exactly, given   and  where  terminates in quadrant IV and  terminates in quadrant III. Be sure to reduce your final result completely.

Answer 1

This is a question which is intended to trip you up with basically non-essential items...so be careful!

cos(a+b) = cos a cos b - sin a sin b.

The magnitude of sin of a is sqrt(16-9)/4 and in quadrant 4 the sin is negative.

The magnitude of cos b is sqrt(49-36)/7 and in quadrant 3 the cos is negative.

Now you plug in the values (CAREFUL with the signs!) to get the answer.

P.S. I got those magnitudes using the Theorem of Pythagoras.

P.P.S. You might like to remember the mnemonic "AllSinTanCos" which tells you which trig functions are positive in quadrant 1,2,3,4.