Mathematics: If cosθ=1/3 , then sinθ = .

If cosθ=1/3 , then sinθ = . - id136464391, roadrnr5183

fredgk

26.01.2022

$sin\theta=\frac{2 \sqrt{2} }{3 }$

Step-by-step explanation:

We can use the following trigonometric property that relates the sine function and the cosine function:

$sin^2\theta+cos^2\theta=1$

we solve for $sin \theta$ :

$sin^2\theta=1-cos^2\theta\\\\sin\theta=\sqrt{1-cos^2\theta}$

we are give the value of $cos\theta$ :

$cos\theta =\frac{1}{3}$

so we substitute this value:

$sin\theta=\sqrt{1-(\frac{1}{3} )^2}$

and we solve the expression:

$sin\theta=\sqrt{1-\frac{1}{9} } \\\\sin\theta=\sqrt{\frac{8}{9} } \\\\sin\theta=\frac{\sqrt{8} }{\sqrt{9} } \\\\sin\theta=\frac{2 \sqrt{2} }{3 }$

the answer is: $sin\theta=\frac{2 \sqrt{2} }{3 }$

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dulaneystrode

08.01.2021

and I need points to ask more questions

Step-by-step explanation:

thank you for the points

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