Coterminal angles are those angles who both share same terminal sides.
Here. the Option C: 40° + (360n)° for any whole number n is correct.
To find coterminal angle with a 400° angle.
Coterminal angles are those angles who both share same terminal sides.
Since terminal side can come at same place after one round forward, two round forward etc and one round backward, two round backward thus multiples of 360 or 0 can be added or subtracted.
A full round is of 360°.
If an angle is of [tex]\theta ^\circ[/tex], then [tex]\text{Coterminal angles of\:} \theta^\circ = \theta^\circ \pm 360^\circ n; n \in \mathbb Z[/tex]
Thus, we have:
Coterminal angles of 400 degrees = [tex]400 \pm 360n = 40+360 \pm 360n = 40 \pm 360(n+1); n+1 \in \mathbb Z\\or\\\text{Complementary angles of 400}^\circ = 40^\circ+360n^\circ; n \in \mathbb Z[/tex]
Thus, the Option C: 40° + (360n)° for any integer n is correct.
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