Question

use the (x,y) coordinates in the given figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. \\(\sec 0\\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a. \\(\sec 0 = \square\\) (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize the denominator.) \\(\bigcirc\\) b. the expression is undefined.

Explanation:

Step1: Identify (x,y) for t=0

From the unit circle, at $t=0$, the coordinates are $(1, 0)$.

Step2: Recall secant definition

$\sec t = \frac{1}{\cos t}$, and $\cos t = x$ for unit circle points $(x,y)$.

Step3: Calculate $\cos 0$

$\cos 0 = 1$

Step4: Compute $\sec 0$

$\sec 0 = \frac{1}{\cos 0} = \frac{1}{1} = 1$

Answer:

A. $\sec 0 = 1$