Sophie takes tap and ballet.
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now let's recall that a full circle has 360°, so then 1140 = 360 + 360 + 360 + 60.
namely, 1140 is 3 full-go-around the circle and then it lands on the I Quadrant at 60°. Thus cos(1140°) = cos(60°).
what's that cosine of 60°? Check the picture below.
