Find the cotangent value and corresponding angle on the unit circle
Answer 1
Ella Lewis
We need to find the angle $\theta$ in the unit circle such that $\cot(\theta) = \sqrt{3}$.
Step 1: Recall that $\cot(\theta) = \frac{1}{\tan(\theta)}$ and $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$.
Step 2: Set up the equation $\frac{1}{\tan(\theta)} = \sqrt{3}$, which then gives $\tan(\theta) = \frac{1}{\sqrt{3}}$.
Step 3: Recall that $\tan(30^\circ) = \tan(\frac{\pi}{6}) = \frac{1}{\sqrt{3}}$.
Therefore, the angle $\theta = 30^\circ$ or $\theta = \frac{\pi}{6}$ in radians, since $\cot(30^\circ) = \sqrt{3}$.
Answer 2
Henry Green
We need to find the angle $ heta$ in the unit circle such that $cot( heta) = sqrt{3}$.
Step 1: Recall the definition $cot( heta) = frac{cos( heta)}{sin( heta)}$.
Step 2: Given $cot( heta) = sqrt{3}$, we have $frac{cos( heta)}{sin( heta)} = sqrt{3}$.
Step 3: This implies $cos( heta) = sqrt{3} sin( heta)$.
Step 4: For known angles, $cos(30^circ) = sqrt{3}/2$ and $sin(30^circ) = 1/2$.
Therefore, the angle $ heta = 30^circ$ or $ heta = frac{pi}{6}$ in radians, since $cot(30^circ) = sqrt{3}$.
Answer 3
Emma Johnson
Find the angle $ heta$ where $cot( heta) = sqrt{3}$.
Since $cot( heta) = frac{cos( heta)}{sin( heta)}$ and the known value of $cot(30^circ) = sqrt{3}$, we find that:
$ heta = 30^circ$ or $ heta = frac{pi}{6}$ in radians.
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