We have two responses for you.
Hi Christina,
I drew a rough sketch of y = cos t for 0 ≤ t ≤ 360 degrees. You can see from the graph that cos t = 1 if t = 0 or t = 360.
You also know from the periodic nature of the cosine function that cos t = 1 if
t = 0, t = 360, t = 2 360 = 720, ...
Thus for your function cos 2x = 1 if 2x = 0, 2x = 360, 2x = 2 360 = 720, .... That is x = 0, x = 180, x = 360, ... But you only want values of x that satisfy 0 ≤ x < 360 and hence the only values are x = 0 degrees and x = 180 degrees.
Penny
Hi Christina.
Try substituting for 2x.
Let = 2x. Then cos = cos 2x. Also, x = /2.
So if 0 <= x < 360, then 0 <= /2 < 360, which means 0 <= < 720.
Now within the range of 0 <= < 720, for what values of is cos = 1?
You can sketch a cosine curve if you can't answer immediately, or look in your textbook for one.
Now that you know all the value(s) of , recall that x = /2, so you can find
each corresponding value for x.
Hope this helps,
Stephen La Rocque. >
