Answer :
Final Answer:
The equation χ = 100 = sin x has 62 real solutions. Therefore, the correct answer is option (B) 62.
Explanation:
The equation χ = 100 = sin x has 62 real solutions. To understand why, consider the graph of the sine function. It oscillates between -1 and 1 infinitely as x varies. When we set χ = 100, we are essentially looking for the points where the sine curve intersects the horizontal line at y = 100.
Now, as the sine curve oscillates, it will intersect the line y = 100 multiple times. Each time it crosses the line, it corresponds to a real solution of the equation. Since the sine function repeats its pattern every 360 degrees (2π radians), it will intersect the line 100 times in a complete cycle. However, the sine function continues indefinitely, so it will keep intersecting the line beyond one cycle.
Therefore, the total number of real solutions to the equation is the number of times the sine curve crosses the line y = 100, which is 100 times for each cycle plus additional intersections as it continues indefinitely. This adds up to 62 intersections in total.
Therefore, the correct answer is option (B) 62.
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