Simplify sin 480 degrees

Answer 1

the trig functions repeat every revolution of the unit circle

so just subtract units of 360º until the angle is less than 360º

480º - 360º = 120º ... this is the angle on the unit circle

sin(480º) = sin(120º)

Answer 2

and

120° = 180° - 60°

sin (180° - θ ) = sin θ

sin 120° = sin (180° - 60° ) = sin 60° = √3 / 2

sin 480° = sin 120°

sin 480° = √3 / 2