On the unit circle, find the values of angles in radians for which the $sec$ function is undefined.
Answer 1
Samuel Scott
The secant function $\sec(\theta)$ is undefined when the cosine function $\cos(\theta)$ is zero. On the unit circle, $\cos(\theta)$ is zero at the points where the x-coordinate is zero, which happens at $\theta = \frac{\pi}{2} + k\pi$ for any integer $k$.
Therefore, the angles in radians for which the secant function is undefined are:
$\theta = \frac{\pi}{2} + k\pi$
where $k \in \mathbb{Z}$ (any integer).
Answer 2
Charlotte Davis
We need to find the values of $ heta$ for which $sec( heta) = frac{1}{cos( heta)}$ is undefined. This occurs when the denominator $cos( heta)$ is zero. On the unit circle, $cos( heta)$ is zero at the points where the angle $ heta$ points to the top or bottom of the circle.
The specific angles in radians are:
$ heta = frac{pi}{2} + kpi,: k in mathbb{Z}$
Answer 3
Isabella Walker
The secant function $sec( heta)$ is undefined when $cos( heta) = 0$. This occurs at:
$ heta = frac{pi}{2} + kpi,: k in mathbb{Z}$
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