Question

rewrite the expression in terms of the given angles reference angle; then evaluate the result. write the exact answer. do not round. sec(14π)

Explanation:

Step1: Find equivalent angle in one - full - rotation

Since the period of the secant function \(y = \sec(x)\) is \(2\pi\), we divide the given angle \(14\pi\) by \(2\pi\). \(14\pi\div2\pi = 7\), which means \(14\pi\) is equivalent to \(0\) radians after considering full - rotations (\(14\pi=7\times2\pi + 0\)).

Step2: Recall the definition of secant

The secant function is defined as \(\sec(x)=\frac{1}{\cos(x)}\). So, \(\sec(14\pi)=\sec(0)\).

Step3: Evaluate cosine at the angle

We know that \(\cos(0) = 1\).

Step4: Evaluate secant

Since \(\sec(x)=\frac{1}{\cos(x)}\), then \(\sec(0)=\frac{1}{\cos(0)}=\frac{1}{1}=1\).

Answer:

\(1\)