use the (x,y) coordinates in the given figure to find the value of the trigonometric function at the…
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 2π select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. sec 2π = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize the denominator.) b. the expression is undefined.
Answer
Explanation:
Step1: Recall secant - cosine relationship
The secant function is defined as $\sec t=\frac{1}{\cos t}$.
Step2: Find the value of $\cos 2\pi$
On the unit - circle, for $t = 2\pi$, the $(x,y)$ coordinates of the corresponding point are $(1,0)$. The cosine of an angle $t$ in standard position on the unit - circle is given by the $x$ - coordinate of the point where the terminal side of the angle intersects the unit - circle. So, $\cos 2\pi=1$.
Step3: Calculate $\sec 2\pi$
Since $\sec 2\pi=\frac{1}{\cos 2\pi}$ and $\cos 2\pi = 1$, then $\sec 2\pi=\frac{1}{1}=1$.
Answer:
A. $\sec 2\pi = 1$