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If \(\tan \theta = \frac{12}{5}\), what is the value of \(1+\sin\theta\)?

  • A.17/13
  • B.18/13
  • C.22/13
  • D.25/13

Answer: D

If \(\tan \theta = 12/5\) (Opposite/Adjacent), we find the hypotenuse: \(Hyp = \sqrt{12^2+5^2} = \sqrt{144+25} = \sqrt{169} = 13\).

\(\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{12}{13}\).

The expression is \(1 + \frac{12}{13} = \frac{13+12}{13} = \frac{25}{13}\).

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