Question 550210
my problem is that as i tried to figure this out.. i got confused in this part
"sin[(&#952;+&#960;)+&#960;/2]" <----- how did it arrived to "cos(&#952;+&#960;)"
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Think of rotating reference angle &#952; in quadrant I, &#960; radians which places the reference angle in quadrant  III. Then rotate angle (&#952;+&#960;) another &#960;/2 radians which places the reference angle in quadrant IV. But this last reference angle is the compliment of (&#952;+&#960;), thus it converts from sin to cos.
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This can be made clearer by an example as follows:
let &#952;=30º in quadrant I, reference angle=30º
30+&#960;=210ºin quadrant III, reference angle=30º
210+&#960;/2=300º in quadrant IV, reference angle=60º
So,sin[(30+&#960;)+&#960;/2]=cos(30+&#960;)

hope this helps.