Question 1084511
True or false: sin (x-180) = sin (180-x)

Could you explain this using the unit circle?

Sincerely,
Just a student trying to learn some maths
<pre>The question is: "Is sin (x – 180) = sin (180 – x)?"

Look at the UNIT CIRCLE anywhere online and you'll see that cos 180 = - 1, and sin 180 = 0

sin (x – 180) = sin x cos 180 – cos x sin 180 --- Difference of angles' identity
sin (x – 180) = sin x * - 1 – cos x * 0 --------- Substituting – 1 for cos 180, and 0 for sin 180
sin (x – 180) = - sin x cos 180 – 0
sin (x – 180) = - sin x

sin (180 – x) = sin 180 cos x – cos 180 sin x --- Difference of angles' identity
sin (180 – x) = 0 * cos x – - 1 * sin x --------- Substituting 0 for sin 180, and – 1 for cos 180
sin (180 – x) = 0 + sin x
sin (180 – x) = sin x

Since: {{{highlight_green(matrix(1,3, - sin (x) <> sin (x), then, sin (x - 180) <> sin (180 - x)))}}}. 
The assertion is therefore {{{highlight_green(FALSE)}}}.