Question

If cosθ=1/3 , then sinθ = _____.

Answer 1

Answer:

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

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