Quèstion 3
Use an addition or subtraction formula to find the exact value of the expression.
$\sin \left(-705^{\circ}\right)$
a. $\frac{-\sqrt{6}+\sqrt{2}}{4}$
b. $\frac{\sqrt{6}+\sqrt{2}}{4}$
$\frac{\sqrt{6}-\sqrt{2}}{4}$

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 \(\boxed{\frac{\sqrt{6}-\sqrt{2}}{4}}\).