Step 1 :Convert the angle from degrees to radians. The Python math library works with radians, so we need to convert the angle before we can use the sin function.
Step 2 :Calculate the sine of the angle using the sin function from the Python math library. The sine of -705 degrees is approximately 0.259.
Step 3 :Compare the calculated sine value with the given options. We can calculate the value of each option and compare it with the calculated sine value.
Step 4 :Calculate the value of each option. The values of the options are approximately -0.259, 0.966, and 0.259, respectively.
Step 5 :Compare the calculated values with the given options. The correct answer is the option that matches the calculated sine value.
Step 6 :The exact value of the expression \(\sin \left(-705^{\circ}\right)\) is \(\boxed{\frac{\sqrt{6}-\sqrt{2}}{4}}\).