Question

given: tan theta = 6/4 find sin theta​

Answer 1

Answer:

$sin \alpha = \frac{4}{6}$

Answer 2

Step-by-step explanation:

$let \: tan \: theta \: = tan \alpha \\ \tan( \alpha ) = \frac{6}{4} = \frac{opp}{adj } \\ by \: pythagoras \: theorem \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} \\ hyp = \sqrt{ {6}^{2} + {4}^{2} } \\ hyp = \sqrt{36 + 16} \\ hyp = \sqrt{52} \\ hyp = \sqrt{4 \times 13} \\ hyp = 2 \sqrt{13} \\ \sin( \alpha ) = \frac{opp}{hyp} \\ \sin( \alpha ) = \frac{6}{2 \sqrt{13} } \\ \sin( \alpha ) = \frac{3}{ \sqrt{13} }$