Tangents \( P A \) and \( P B \) are drawn to the circle \( (x-4)^{... VIDEO
Tangents \( P A \) and \( P B \) are drawn to the circle \( (x-4)^{2}+(y-5)^{2}=4 \)
\( \mathrm{P} \) from the point \( P \) on the curve \( y=\sin x \), where \( A \) and \( B \) lie on the
W circle. Consider the function \( y=f(x) \) represented by the locus of the center of the circumcircle of triangle \( P A B \). Then answer the following questions.
The range of \( y=f(x) \) is
(1) \( [-2,1] \)
(2) \( [-1,4] \)
(3) \( [0,2] \)
(4) \( [2,3] \)
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