Solutions To Exercises Functions Worksheet Page 13
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13Solutions to Exercises
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Exercise 5. Show that the period of the tangent and cotangent function is π.
Solution: We have already seen that tan (t + π) = tan t for all numbers t in the
domain of the tangent function. It remains to show that π is the smallest such
number. Suppose there is a number c such that tan (t + c) = tan t for all t in the
domain of the tangent function. Then setting t = 0 yields
tan 0 = tan c
suggesting that c is an integer multiple of π. It follows that π is the smallest positive
number for which tan (t + π) = tan t for all numbers t in its domain. Since the
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cot t =
it follows that the cotangent function also has period π.
Exercise 5
tan t
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