Find the value of $cot( heta)$ given that $ heta$ is a point on the unit circle where $cos( heta) = a$ and $sin( heta) = b$.
Answer 1
Lucas Brown
Since $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$, we can use the given values of $\cos(\theta)$ and $\sin(\theta)$.
Given that $\cos(\theta) = a$ and $\sin(\theta) = b$, we plug these into the cotangent formula:
$\cot(\theta) = \frac{a}{b}$
Therefore, the value of $\cot(\theta)$ is $\frac{a}{b}$.
Answer 2
Christopher Garcia
To find $cot( heta)$, we start with the identity $cot( heta) = frac{1}{ an( heta)}$.
The tangent function is defined as $ an( heta) = frac{sin( heta)}{cos( heta)}$.
Given that $cos( heta) = a$ and $sin( heta) = b$, we find that:
$ an( heta) = frac{b}{a}$
Thus,
$cot( heta) = frac{1}{frac{b}{a}} = frac{a}{b}$
Answer 3
John Anderson
Given $cos( heta) = a$ and $sin( heta) = b$,
$cot( heta) = frac{a}{b}$
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