Answer:
The correct option is B) [tex]sin\theta=\frac{\sqrt{5}}{3}[/tex] and [tex]tan\theta=\frac{\sqrt{5}}{2}[/tex]
Step-by-step explanation:
given [tex]cos\theta=-\frac{2}{3}[/tex]
Since, [tex]cos\theta=\frac{base}{hypoteneous}[/tex]
it means prependicular of right angled triangle can be calculated by pythagoras theorem as:
base² + prependicular² = hypoteneous²
2² + prependicular² = 3²
4 + prependicular² = 9
prependicular² = 9 - 4
prependicular² = 5
prependicular = √5
Since, [tex]sin\theta=\frac{prependicular}{hypoteneous}[/tex]
[tex]sin\theta=\frac{\sqrt{5}}{3}[/tex]
Since, [tex]tan\theta=\frac{prependicular}{base}[/tex]
[tex]tan\theta=\frac{\sqrt{5}}{2}[/tex]
Hence, the correct option is B) [tex]sin\theta=\frac{\sqrt{5}}{3}[/tex] and [tex]tan\theta=\frac{\sqrt{5}}{2}[/tex]
