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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 11.3, Problem 33E
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Elementary Geometry for College St...

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

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
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
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In Exercises 33 to36, 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 ≠ 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.

Chapter 11.3, Problem 33E, In Exercises 33 to36, we expand the list of trigonometric identities. As you may recall, an identity

To determine

(a)

To prove:

For α≠90∘, the identity tanα=sinαcosα.

Explanation

Given:

For α≠90∘, tanα=sinαcosα.

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

tanα=ab   ...(1)

Consider sinαcosα.

To determine

(b)

To show:

The trigonometric ratio tan23∘ is equivalent to sin23∘cos23∘ using calculator.

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