A) \[-\frac{4}{5}\] but not \[\frac{4}{5}\]
B) \[-\frac{4}{5}\] or \[\frac{4}{5}\]
C) \[\frac{4}{5}\] but not \[-\frac{4}{5}\]
D) None of these
Correct Answer: B
Solution :
\[\tan \theta \] is negative in second and fourth quadrants. Since, \[\tan \theta =-\frac{4}{3}\] \[\therefore \] \[h=\sqrt{16+9}=\sqrt{25}\Rightarrow h=5\] \[\therefore \] \[\sin \theta =\frac{4}{5}\]
But \[\tan \theta \] is negative which is possible only, if \[\theta \] lies in second and fourth quadrants. \[\therefore \sin \theta \] may be \[\frac{4}{5}\] or \[-\frac{4}{5}\].
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