Question

If cosθ=1/3 , then sinθ = _____.

Answer 1

`sin\theta=(2 √(2) )/(3 )`

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=√(1-cos^2\theta)`

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

`cos\theta =(1)/(3)`

so we substitute this value:

`sin\theta=\sqrt{1-((1)/(3) )^2}`

and we solve the expression:

`sin\theta=\sqrt{1-(1)/(9) } \\\\sin\theta=\sqrt{(8)/(9) } \\\\sin\theta=(√(8) )/(√(9) ) \\\\sin\theta=(2 √(2) )/(3 )`

the answer is:
`sin\theta=(2 √(2) )/(3 )`