<p>How do you show that cos(360-A) = cos A?</p>
<p>I solved this with several numbers in order to come up with a sort of idea. I think it relates to the unit circle since say you choose A to be 45 degrees…</p>
<p>A= 45 degrees and 360-45=315 degrees OR -45 (same thing). Both form the same angle with the X-axis (of 45 degrees). If you do (Cos 45)^2 + Cos (360-45)^2 it =1. 1 is also the hypotenuse/length of all unit circle lines. </p>
<p>I apologize if this is a lame connection, but I think it is related to the fact that any angle measure and 360 minus that angle measure still form the same sized angle with the X-axis so their cosines would therefore be the same.</p>
<p>You could draw it out… (360-A) is the same as (-A), so then you’re proving cos(-A)=cos(A).</p>
<p>Cosine is an even function, and by that cos(-A)=cos(A). Also, if A is in the first quadrant, negative A is in the fourth quadrant, and since cosine is positive in both Quad. I and Quad. IV, the negative sign has no effect. If A is in the second quadrant, negative A is in the third quadrant, and cosine is negative in both of those.</p>
<p>Hope this helps.</p>