Answer:
[tex]sin\theta=\frac{2 \sqrt{2} }{3 }[/tex]
Step-by-step explanation:
We can use the following trigonometric property that relates the sine function and the cosine function:
[tex]sin^2\theta+cos^2\theta=1[/tex]
we solve for [tex]sin \theta[/tex]:
[tex]sin^2\theta=1-cos^2\theta\\\\sin\theta=\sqrt{1-cos^2\theta}[/tex]
we are give the value of [tex]cos\theta[/tex]:
[tex]cos\theta =\frac{1}{3}[/tex]
so we substitute this value:
[tex]sin\theta=\sqrt{1-(\frac{1}{3} )^2}[/tex]
and we solve the expression:
[tex]sin\theta=\sqrt{1-\frac{1}{9} } \\\\sin\theta=\sqrt{\frac{8}{9} } \\\\sin\theta=\frac{\sqrt{8} }{\sqrt{9} } \\\\sin\theta=\frac{2 \sqrt{2} }{3 }[/tex]
the answer is: [tex]sin\theta=\frac{2 \sqrt{2} }{3 }[/tex]
