Find the value of $ cot( heta) $ when $ heta = frac{pi}{4} $ on the unit circle.
Answer 1
John Anderson
Given:
\( \theta = \frac{\pi}{4} \)
On the unit circle, the coordinates for \( \theta = \frac{\pi}{4} \) are:
\( (\cos(\frac{\pi}{4}), \sin(\frac{\pi}{4})) = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) \)
\( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \)
Substituting the values:
\( \cot(\frac{\pi}{4}) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 \)
Therefore, \( \cot(\frac{\pi}{4}) = 1 \).
Answer 2
Isabella Walker
For ( heta = frac{pi}{4} ) on the unit circle:
The corresponding coordinates are ( (cos(frac{pi}{4}), sin(frac{pi}{4})) = (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) ).
By definition, ( cot( heta) = frac{cos( heta)}{sin( heta)} ).
Thus, ( cot(frac{pi}{4}) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 ).
Hence, ( cot(frac{pi}{4}) = 1 ).
Answer 3
Thomas Walker
Given ( heta = frac{pi}{4} ) on the unit circle:
( cos(frac{pi}{4}) = sin(frac{pi}{4}) = frac{sqrt{2}}{2} )
( cot(frac{pi}{4}) = frac{cos(frac{pi}{4})}{sin(frac{pi}{4})} = 1 )
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