   Chapter 11.3, Problem 35E 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 ≠ 90 ∘ , prove the identity sec α = 1 cos α . b) Use your calculator to determine sec 82 ∘ . To determine

(a)

To prove:

For α90, the identity secα=1cosα.

Explanation

Given:

For α90, secα=1cosα.

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.

cosα=bc

secα=cb   ...(1)

Consider 1cosα.

To determine

(b)

To find:

The value of sec82 using the calculator.

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