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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 11.3, Problem 34E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Problem 1E
Problem 2E
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Problem 10E
Problem 11E
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Problem 15E
Problem 16E
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Problem 18E
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Problem 20E
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Problem 23E
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Problem 25E
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Problem 31E
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Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

In Exercises 33 to 36, we expand the list of trigonometric identities. As you may recall, an identity is a statement that is true for all permissible choices of the variable (see page 502.)

a) For α ≠ 0 ∘ , prove the identity cot α = cos α sin α .

b) Use your calculator to determine cot 57 ∘ by dividing cos 57 ∘ by sin 57 ∘ .

Chapter 11.3, Problem 34E, In Exercises 33 to 36, we expand the list of trigonometric identities. As you may recall, an

To determine

(a)

To prove:

For α≠0∘, the identity cotα=cosαsinα.

Explanation

Given:

For α≠0∘, cotα=cosαsinα.

Definition used:

The trigonometric ratios:

sinα=oppositehypotenuse
cosα=adjacenthypotenuse
tanα=oppositeadjacent

Calculation:

Consider the angle α.

From the figure, the length of the opposite leg is a, the length of the adjacent leg is b and the hypotenuse is c.

sinα=ac

cosα=bc

cotα=1tanα=ba   ...(1)

Consider cosαsinα

To determine

(b)

To show:

The trigonometric ratio cot57∘ is equivalent to cos57∘sin57∘ using calculator.

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Chapter 11.3,
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Sect-11.1 P-1ESect-11.1 P-2ESect-11.1 P-3ESect-11.1 P-4ESect-11.1 P-5ESect-11.1 P-6ESect-11.1 P-7ESect-11.1 P-8ESect-11.1 P-9ESect-11.1 P-10E
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