what happens when you add 4pi to an angle?

Answer 1

it goes around the circle twice, therefore it is a coterminal angle to the original angle. all trig values are the same. the only difference is that the degrees goes up by 720.

adding or subtracting multiples of 2 pi just go around the circle. since pi=180 degrees, add or subtract 180*the number of pi's.

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Answer 2

a full circle is 2pi radians

so 4pi is two complete turns

so if you have an angle, alpha, then sin(alpha) is equal to sin(alpha+2pi), is equal to sin(alpha+4pi), and so on

which is why, when people solve trigonometry problems properly, they never express their solution as, say "alpha = 0.64 radians", but rather, as "alpha = 0.64 + 2kpi, where k is any integer)

Answer 3

Since 2 pi radians is 180 degrees - 4 pi would bring you right back to where you started. You sorta went full cicle...