Find the exact value of $ an( heta)$ given the point on the unit circle
Answer 1
Matthew Carter
Given a point on the unit circle at $(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$, find the exact value of $\tan(\theta)$.
First, identify the coordinates $x$ and $y$ from the point, which are $x = -\frac{1}{2}$ and $y = -\frac{\sqrt{3}}{2}$ respectively. Recall that $\tan(\theta) = \frac{y}{x}$.
Plug in the values of $x$ and $y$:
$\tan(\theta) = \frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}} = \frac{\sqrt{3}}{1} = \sqrt{3}$
Therefore, the exact value of $\tan(\theta)$ is $\sqrt{3}$.
Answer 2
Ella Lewis
Given the point $(-frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle, find $ an( heta)$.
Identify the coordinates: $x = -frac{1}{2}$ and $y = frac{sqrt{3}}{2}$. Recall that $ an( heta) = frac{y}{x}$.
Thus,
$ an( heta) = frac{frac{sqrt{3}}{2}}{-frac{1}{2}} = -sqrt{3}$
The exact value of $ an( heta)$ is $-sqrt{3}$.
Answer 3
Lily Perez
Given the point $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$ on the unit circle, find $ an( heta)$.
Here, $x = frac{sqrt{2}}{2}$ and $y = frac{sqrt{2}}{2}$.
Therefore,
$ an( heta) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$
The exact value of $ an( heta)$ is $1$.
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