Determine the exact value of
sin(−135)°.

identify the reference angle, theta

theta=?

-135° is in quadrant 3 (going clockwise rather than counter-clockwise as we usually do). The reference angle is 45° degrees (the terminal arm is 45° from the x-axis).
To find the exact value, use the special triangles. sin(45°)=√2÷2 (rationalized form of 1÷√2, which you can get from the triangle: it has two sides of value 1, and by the Pythagoras theorem we get √2 as the hypotenuse; SOHCAHTOA gives us 1÷√2 for the sine value).The exact value of sin(-135°) would be -(√2÷2). (-135° is equivalent to 225°. sin(225°) does give the same answer as the negative of sin(45°)).