The sine of 140 degrees and the sine of 40 degrees are indeed equal due to a property of the sine function in trigonometry. This property states that:
sin(θ) = sin(180° – θ)
In this case, if we take θ to be 40 degrees, we can find:
sin(140°) = sin(180° – 140°) = sin(40°)
This relationship occurs because of the symmetry of the unit circle. When you look at an angle in the second quadrant (like 140 degrees), it corresponds to a positive sine value that is equal to its reference angle in the first quadrant (which is 40 degrees). Therefore, both angles share the same sine value. In summary, the sine values are the same because they are reflections across the y-axis in the unit circle.