Question

Please help, I don't understand

Answer 1

sin(θ) = (2/5)√6

Explanation:

The sine and cosine are related by the formula ...

`sin((\theta))^2+cos((\theta))^2=1\\\\sin((\theta))=\pm√(1-cos((\theta))^2)`

Filling in the given value for cos(θ), we find the sine to be ...

`sin((\theta))=\pm\sqrt{1-\left((1)/(5)\right)^2}=\pm(√(24))/(5)=\pm(2)/(5)√(6)`

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The cosine function is positive for angles in both the first and fourth quadrants. The restriction on θ tells us this is a first-quadrant angle. The sine is positive in the first quadrant, so the desired value is ...

sin(θ) = (2/5)√6