Let be the number of real roots of the above equation if is measured in degrees.
Let be the number of real roots of the above equation if is measured in radians.
Find the value of ?
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If we graph the line given by y = 1 0 0 x and the curve y = sin ( x ) , the number of points they have in common is what we require.
When x is measured in degrees , it can be easily seen that the line intersects sine graph at 2 distinct points and the origin , that is 3 in total.Thus A = 3 .
Now consider when x is measured in radians . Since y = 1 0 0 x , as value of y exceeds 1 , the line goes away from the sine curve and doesnot intersect.Let x = k π for some real k such that 1 0 0 k π = 1 ⇒ k = π 1 0 0 ≈ 2 2 7 0 0 ≈ 3 1 . 8 . Since 3 1 π < 3 1 . 8 π < 3 2 π , the last point that the line intersects lies on the part of curve that terminates on 3 1 π . Thus the line intersects the curve at 3 1 distinct points on right side of Y axis. By symmetry , it also intersects the curve at 3 1 distinct points on left side of Y axis. Origin is also common point to the line and curve. And hence B = 3 1 + 3 1 + 1 = 6 3 .
Thus A + B = 3 + 6 3 = 6 6 .