   Chapter 11.3, Problem 36E 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 csc α = 1 sin α . b) Use your calculator to determine csc 12.3 ∘ . To determine

(a)

To prove:

For α0, the identity cscα=1sinα.

Explanation

Given:

For α0, cscα=1sinα.

Definition used:

The trigonometric ratios:

 sinα=oppositehypotenuse cosecα=hypotenuseopposite

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

cscα=ca   ...(1)

Consider 1sinα.

To determine

(b)

To find:

The value of csc12.3 using the calculator.

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