Sin480° convert to surds form

Answer 1

To convert sin 480° to surds form, we can use the fact that sin (180° + x) = -sin x.

First, let's find the equivalent angle in the range 0° to 360°:
480° = 360° + 120°

Now, we can rewrite the sin 480° as sin (360° + 120°):
sin 480° = -sin 120°

Next, let's use the fact that sin (180° - x) = sin x to rewrite sin 120°:
sin 120° = sin (180° - 60°) = sin 60°

Lastly, we know that sin 60° = √3/2 in surds form, so the final answer is:
sin 480° = -sin 120° = -sin 60° = -√3/2 in surds form.