determine an exact expression for the trigonometric function sin(13pi/12).

Answer 1

note that 13pi/12 is also 195 degrees, which can be expressed as difference of two angles, 240 - 45:
sin(13pi/12) = sin(195) = sin(240-45)
*expanding this,
sin(240)cos(45)-cos(240)sin(45)
(-sqrt(3)/2)(sqrt(2)/2)-(-1/2)(sqrt(2)/2)
(-sqrt(6)/4)+(sqrt(2)/4)
therefore:
{[sqrt(2)-sqrt(6)]/4}

so there,, :)