Question

Henrik the meerkat, the friend of Gottfried and Bernhardt, says that if an angle in radians is larger than 2pi, then the sine of the angle is larger than 1 . Bernhard disagrees, and says that no matter what the radian measure of an angle is, the sine of that angle is always between -1 and 1. Who is correct and why?
Please help and thank you!!

Answer 1

When angles are restricted to real numbers, Bernhard is correct. The sine function has a range of -1 to 1 (inclusive).

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When angles are allowed to be complex numbers, the magnitude of the sine of an angle may exceed 1. In this realm, both Henrik and Bernhard are incorrect.

Answer 2

The sine function, defined for all x, is always between -1 and +1. It begins at (0,0), increases to 1 at x = pi/2, decreases to -1 at x = 3pi/2, and increases to 0 as x reaches pi. Thus, the range is [-1,1], regardless of the value of x. Bernie is correct. Gottfried got fried.