Final answer:
The value of x that satisfies the equation sin x = 0.643 is 40° because the sum of the angles in a right triangle is 90°, so sin(40°) is equal to cos(50°).
Step-by-step explanation:
If "cos 50° = 0.643", then we are asked to determine the angle x where "sin x = 0.643". The sine function yields positive values in the first and second quadrants, so there are two possible angles where the sine value could be 0.643: one in the first quadrant and one in the second quadrant. Since the cosine and sine functions are cofunctions, when cos(A) = sin(B), the angles relate as A + B = 90°. Considering that we initially have cos(50°), it would mean that sin(40°) will also be 0.643 because 50° + 40° = 90°. Thus, the value of x that makes sin x equal to 0.643 is 40°.