Question

Please help, I don't understand

Answer 1

Answer:

  sin(θ) = (2/5)√6

Step-by-step explanation:

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

  $\sin{(\theta)}^2+\cos{(\theta)}^2=1\\\\\sin{(\theta)}=\pm\sqrt{1-\cos{(\theta)}^2}$

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

  $\sin{(\theta)}=\pm\sqrt{1-\left(\dfrac{1}{5}\right)^2}=\pm\dfrac{\sqrt{24}}{5}=\pm\dfrac{2}{5}\sqrt{6}$

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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