Given,
The equation is,
[tex]sin\theta=\frac{3\sqrt{10}}{10}[/tex]
Required
The value of tan theta.
The value of cos theta is,
[tex]\begin{gathered} cos\theta=\sqrt{1-(\frac{3\sqrt{10}}{10}})^2 \\ =\sqrt{1-\frac{90}{100}} \\ =\sqrt{\frac{10}{100}} \\ =-\frac{\sqrt{10}}{10} \end{gathered}[/tex]
The value of tan theta is,
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ =\frac{3\sqrt{10}}{10}\times\frac{-10}{\sqrt{10}} \\ =-3 \end{gathered}[/tex]
Hence, the value of tan theta is -3.
