Question

evaluate the six trigonometric function of \\( \theta \\). (hint: sketch the angle and use your unit circle) if the ratio is undefined, enter dne.

\\( \theta = 540 ^ { \circ } \\)

Explanation:

Step1: Find the coterminal angle

Subtract \(360^{\circ}\) from \(540^{\circ}\).
\(540^{\circ}- 360^{\circ}=180^{\circ}\)

Step2: Evaluate \(\cos\theta\)

Using the unit - circle, for \(\theta = 180^{\circ}\), \(\cos\theta=-1\)

Step3: Evaluate \(\sec\theta\)

Since \(\sec\theta=\frac{1}{\cos\theta}\), and \(\cos\theta=-1\), then \(\sec\theta=\frac{1}{-1}=-1\)

Answer:

\(\cos\theta=-1\), \(\sec\theta = - 1\)