Chapter 6: Q. 122 (page 397)

Show that the range of the cotangent function is the set of all
real numbers.

Short Answer

Expert verified

The range of cotangent function is a set of real numbers.

Step by step solution

Step 1. Given Information

A co-tangent function.

Step 2. Explanation

$C o n s i d e r c o t = \frac{x}{y} a = \frac{x}{y} x = a y B u t, x^{2} + y^{2} = 1 a^{2} y^{2} + y^{2} = 1 y = \pm \frac{1}{\sqrt{a^{2} + 1}} t h e r e f o r e t h e v a l u e o f x i s x = a y = a \times \pm \frac{1}{\sqrt{a^{2} + 1}} = \pm \frac{a}{\sqrt{a^{2} + 1}} t h u s f o r s n y r e a l n u m b e r a, t h e r e i s a p o i n t p (x, y) f o r w h i c h c o t t = a i . e . - \infty < c o t t < \infty t h u s r a n g e o f c o \tan g e t f u n c t i o n i s s e t o f a l l r e a l n u m b e r s .$

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Show that the range of the cotangent function is the set of all
real numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Show that the range of the cotangent function is the set of allreal numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Show that the range of the cotangent function is the set of all
real numbers.