Answer:
B. [tex]\sin \theta=\frac{-\sqrt{5}}{3}[/tex] and [tex]\tan \theta =\frac{\sqrt{5}}{2}[/tex]
Step-by-step explanation:
We are given that,
[tex]\cos \theta=\frac{-2}{3}[/tex].
Since, we know,
[tex]\sin^2 \theta+\cos^2 \theta=1[/tex]
i.e. [tex]\sin^2 \theta=1-\cos^2 \theta[/tex]
i.e. [tex]\sin^2 \theta=1-(\frac{-2}{3})^2[/tex]
i.e. [tex]\sin^2 \theta=1-\frac{4}{9}[/tex]
i.e. [tex]\sin^2 \theta=\frac{9-4}{9}[/tex]
i.e. [tex]\sin^2 \theta=\frac{5}{9}[/tex]
i.e. [tex]\sin \theta=\pm \frac{\sqrt{5}}{3}[/tex]
Also, we get,
[tex]\tan \theta =\frac{\sin \theta}{\cos \theta}[/tex]
i.e. [tex]\tan \theta =\frac{\pm \frac{\sqrt{5}}{3}}{\frac{-2}{3}}[/tex]
i.e. [tex]\tan \theta =\mp \frac{\sqrt{5}}{2}[/tex]
So, we get that,
Option B is correct.
