   Chapter 11.3, Problem 33E 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 tan α = sin α cos α (HINT: sin α = a c and cos α = b c . )b) Use your calculator to show that tan 23 ∘ and sin 23 ∘ cos 23 ∘ are equivalent. To determine

(a)

To prove:

For α90, the identity tanα=sinαcosα.

Explanation

Given:

For α90, tanα=sinαcosα.

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

tanα=ab   ...(1)

Consider sinαcosα.

To determine

(b)

To show:

The trigonometric ratio tan23 is equivalent to sin23cos23 using calculator.

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