Find the value of $cot left( frac{pi}{4}
ight)$ on the unit circle.
Answer 1
James Taylor
To find $\cot \left( \frac{\pi}{4} \right)$, we use the definition of cotangent in terms of sine and cosine.
$\cot \theta = \frac{\cos \theta}{\sin \theta}$
For $\theta = \frac{\pi}{4}$, we have:
$\cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$
$\sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$
Therefore,
$\cot \left( \frac{\pi}{4} \right) = \frac{\cos \left( \frac{\pi}{4} \right)}{\sin \left( \frac{\pi}{4} \right)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
Answer 2
Henry Green
Finding $cot left( frac{pi}{4}
ight)$ involves using the unit circle definitions.
On the unit circle, $cot heta = frac{cos heta}{sin heta}$.
Given $ heta = frac{pi}{4}$:
$cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
Thus,
$cot left( frac{pi}{4}
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$
Answer 3
Matthew Carter
We need to find $cot left( frac{pi}{4}
ight)$ using the unit circle.
On the unit circle,
$cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
Then,
$cot left( frac{pi}{4}
ight) = 1$
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