Find the value of sin765o

Rewriting sin765^o,

sin765^o  = sin( 2 x 360^o + 45^o )

After an interval of 2 π, or 360^o, the values of sinx get repeated.

Therefore,

sin765^o = sin( 2 x 360^o + 45^o )

= sin45^o

= 1 / √ 2

Hence, the value of sin765^o is 1 / √ 2