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

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 33 to 38, 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 510.)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 ∘ . To determine

(a)

To prove:

For α0, the identity cotα=cosαsinα.

Explanation

Given:

For α0, cotα=cosαsinα.

Definition used:

The trigonometric ratios:

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 cos57sin57 using calculator.

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