Find $\sin \theta$
\[
\tan \theta=-\frac{\sqrt{10}}{3}, \cos \theta> 0
\]
\[
\sin \theta=
\]
(Use integers or fractions for any numbers in the expression.)
Answer
Final Answer: \(\sin \theta = \boxed{-\frac{\sqrt{10}}{3} \cdot \sqrt{1 - \left(-\frac{\sqrt{10}}{3}\right)^2 / \left(1 + \left(-\frac{\sqrt{10}}{3}\right)^2\right)}}\) or approximately, \(\sin \theta = \boxed{-0.7254762501100117}\)
Step 1 ：Given that \(\tan \theta = -\frac{\sqrt{10}}{3}\) and \(\cos \theta > 0\)
Step 2 ：We know that \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), so we can express \(\sin \theta\) as \(\sin \theta = \tan \theta \cdot \cos \theta\)
Step 3 ：Substitute the given values into the equation to find \(\sin \theta\)
Step 4 ：Final Answer: \(\sin \theta = \boxed{-\frac{\sqrt{10}}{3} \cdot \sqrt{1 - \left(-\frac{\sqrt{10}}{3}\right)^2 / \left(1 + \left(-\frac{\sqrt{10}}{3}\right)^2\right)}}\) or approximately, \(\sin \theta = \boxed{-0.7254762501100117}\)
