Find the value of $cot( heta)$ of an angle on the unit circle
Answer 1
Amelia Mitchell
To find the value of $\cot(\theta)$, we need to use the coordinates of the angle on the unit circle. Let $\theta$ be an angle in the unit circle with coordinates $(\cos(\theta), \sin(\theta))$.
The formula for cotangent is given by:
$\cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)}$
If $\theta = \frac{\pi}{4}$, then $\cos(\frac{\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$.
Thus,
$\cot(\frac{\pi}{4}) = \frac{\cos(\frac{\pi}{4})}{\sin(\frac{\pi}{4})} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
Answer 2
Alex Thompson
To find $cot( heta)$ on the unit circle, recall that $cot( heta) = frac{cos( heta)}{sin( heta)}$.
Using $ heta = frac{pi}{3}$, note that $cos(frac{pi}{3}) = frac{1}{2}$ and $sin(frac{pi}{3}) = frac{sqrt{3}}{2}$.
Therefore,
$cot(frac{pi}{3}) = frac{cos(frac{pi}{3})}{sin(frac{pi}{3})} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
Answer 3
Ella Lewis
For $ heta = frac{pi}{6}$, $cot( heta)$ is:
$cot(frac{pi}{6}) = frac{cos(frac{pi}{6})}{sin(frac{pi}{6})} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3}$
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