Find the coordinates and angle measure for the point on the unit circle where the $sec$ function is undefined.
Answer 1
Christopher Garcia
Let’s start by identifying where the secant function is undefined. Recall that $\sec(\theta) = \frac{1}{\cos(\theta)}$.
The secant function is undefined when $\cos(\theta) = 0$. On the unit circle, this occurs at the points where the x-coordinate is 0. These points are at $\theta = \frac{\pi}{2}$ and $\theta = \frac{3\pi}{2}$.
At $\theta = \frac{\pi}{2}$, the coordinates are $(0, 1)$.
At $\theta = \frac{3\pi}{2}$, the coordinates are $(0, -1)$.
Thus, the secant function is undefined at $\theta = \frac{\pi}{2}$ and $\theta = \frac{3\pi}{2}$, with corresponding coordinates $(0, 1)$ and $(0, -1)$ respectively.
Answer 2
Olivia Lee
To solve this problem, note that $sec( heta) = frac{1}{cos( heta)}$. Therefore, the secant function is undefined when $cos( heta) = 0$. This happens at $ heta = frac{pi}{2}$ and $ heta = frac{3pi}{2}$, where the x-values are zero on the unit circle.
For $ heta = frac{pi}{2}$:
Coordinates: $(0, 1)$
For $ heta = frac{3pi}{2}$:
Coordinates: $(0, -1)$
Thus, the points and angles where the secant function is undefined are $(0, 1)$ at $ heta = frac{pi}{2}$ and $(0, -1)$ at $ heta = frac{3pi}{2}$.
Answer 3
Daniel Carter
The secant function, $sec( heta) = frac{1}{cos( heta)}$, is undefined where $cos( heta) = 0$.
This occurs at $ heta = frac{pi}{2}$ and $ heta = frac{3pi}{2}$, with coordinates $(0, 1)$ and $(0, -1)$ respectively.
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