Convert $frac{5pi}{6}$ radians to degrees and find the sine and cosine values on the unit circle.
Answer 1
Alex Thompson
First, we convert radians to degrees:
$\text{Degrees} = \frac{5\pi}{6} \times \frac{180}{\pi} = \frac{5 \times 180}{6} = 150^{\circ}$
Next, we identify the sine and cosine values for $150^{\circ}$ on the unit circle:
$\sin(150^{\circ}) = \sin(180^{\circ} – 30^{\circ}) = \sin(30^{\circ}) = \frac{1}{2}$
$\cos(150^{\circ}) = \cos(180^{\circ} – 30^{\circ}) = -\cos(30^{\circ}) = -\frac{\sqrt{3}}{2}$
Answer 2
Benjamin Clark
To convert $frac{5pi}{6}$ radians to degrees:
$ ext{Degrees} = frac{5pi}{6} imes frac{180}{pi} = 150^{circ}$
On the unit circle, the coordinates for $150^{circ}$ are obtained by:
$sin(150^{circ}) = sin(180^{circ} – 150^{circ}) = sin(30^{circ}) = frac{1}{2}$
$cos(150^{circ}) = cos(180^{circ} – 30^{circ}) = -cos(30^{circ}) = -frac{sqrt{3}}{2}$
Answer 3
Amelia Mitchell
To convert $frac{5pi}{6}$ radians to degrees:
$frac{5pi}{6} imes frac{180}{pi} = 150^{circ}$
Thus,
$sin(150^{circ}) = frac{1}{2}$
$cos(150^{circ}) = -frac{sqrt{3}}{2}$
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