question 13\ncomplete the following table using exact values. do not rationalize any denominators.\nquestion…

Explanation:

Step1: Recall the reciprocal relationship

The secant function is the reciprocal of the cosine function, i.e., (\sec x=\frac{1}{\cos x}).

Step2: Calculate (\sec x) for (x = 0^{\circ})

Given (\cos0^{\circ}=1), then (\sec0^{\circ}=\frac{1}{\cos0^{\circ}}=\frac{1}{1}=1).

Step3: Calculate (\sec x) for (x = 30^{\circ})

Given (\cos30^{\circ}=\frac{\sqrt{3}}{2}), then (\sec30^{\circ}=\frac{1}{\cos30^{\circ}}=\frac{2}{\sqrt{3}}).

Step4: Calculate (\sec x) for (x = 45^{\circ})

Given (\cos45^{\circ}=\frac{1}{\sqrt{2}}), then (\sec45^{\circ}=\frac{1}{\cos45^{\circ}}=\sqrt{2}).

Step5: Calculate (\sec x) for (x = 60^{\circ})

Given (\cos60^{\circ}=\frac{1}{2}), then (\sec60^{\circ}=\frac{1}{\cos60^{\circ}} = 2).

Step6: Calculate (\sec x) for (x = 90^{\circ})

Given (\cos90^{\circ}=0), then (\sec90^{\circ}=\frac{1}{\cos90^{\circ}}), and division by zero is undefined.

Answer:

(x)	(\cos x)	(\sec x)
(0^{\circ})	(1)	(1)
(30^{\circ})	(\frac{\sqrt{3}}{2})	(\frac{2}{\sqrt{3}})
(45^{\circ})	(\frac{1}{\sqrt{2}})	(\sqrt{2})
(60^{\circ})	(\frac{1}{2})	(2)
(90^{\circ})	(0)	Undefined