complete the following table using exact values. do not rationalize any denominators.\n\nquestion help…

Explanation:

Step1: Recall the reciprocal identity

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})

When (x = 0^{\circ}), (\cos x=1). Then (\sec x=\frac{1}{\cos x}=\frac{1}{1} = 1)

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

When (x = 30^{\circ}), (\cos x=\frac{\sqrt{3}}{2}). Then (\sec x=\frac{1}{\cos x}=\frac{2}{\sqrt{3}})

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

When (x = 45^{\circ}), (\cos x=\frac{1}{\sqrt{2}}). Then (\sec x=\frac{1}{\cos x}=\sqrt{2})

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

When (x = 60^{\circ}), (\cos x=\frac{1}{2}). Then (\sec x=\frac{1}{\cos x}=2)

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

When (x = 90^{\circ}), (\cos x = 0). Then (\sec x=\frac{1}{\cos x}), and division by zero is undefined. So (\sec90^{\circ}) 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