The student's question involves applying trigonometric identities to calculate sin(a + ß), given sin a and cos ß for angles in Quadrant I and III, respectively.
The student is asking about how to apply trigonometric identities to find the sine of a sum of two angles, when the sine of one angle and the cosine of another are given. Specifically, the student has provided the values sin a = 4/5 and cos ß = -24/25, where angle 'a' lies in Quadrant I and angle 'ß' lies in Quadrant III. To find sin(a + ß), we use the identity:
sin (a ± ß) = sin a cos ß ± cos a sin ß
Since we know sin a and cos ß, we need to find cos a and sin ß. We can find these by using the Pythagorean identity sin² a + cos² a = 1 and sin² ß + cos² ß = 1. In Quadrant I, cos a is positive, and in Quadrant III, sin ß is negative. Finally, we substitute these into the identity to compute sin(a + ß).