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!!
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.
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.
