Explanation Pythagorean Identities: 1. sin 2 u + cos 2 u = 1 2. 1 + tan 2 u = sec 2 u 3. 1 + cot 2 u = csc 2 u Calculation: x 2 − 16 Now we can substitute x = 4 sec θ in the above expression x 2 − 16 = ( 4 sec θ ) 2 − 16 Now we can square the terms inside the bracket ( 4 sec θ ) 2 − 16 = 16 sec 2 θ − 16 Since 16 is common in both terms we can take it out

10th Edition

ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosi…

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Chapter 5.CR, Problem 18CR

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To write:

The algebraic expression as a trigonometric function of θ, where 0<θ<π2 by using the trigonometric substitution.

x2−16,x=4secθ

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Chapter 5.CR, Problem 17CR

Chapter 5.CR, Problem 19CR

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The algebraic expression as a trigonometric function of θ , where 0 < θ < π 2 by using the trigonometric substitution. x 2 − 16 , x = 4 sec θ

Solution Summary: The author explains how to write the algebraic expression as a trigonometric function of theta .

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To write:

The algebraic expression as a trigonometric function of θ, where 0<θ<π2 by using the trigonometric substitution.

x2−16,x=4secθ

Want to see the full answer?

Chapter 5 Solutions

The algebraic expression as a trigonometric function of θ , where 0 &lt; θ &lt; π 2 by using the trigonometric substitution. x 2 − 16 , x = 4 sec θ

Solution Summary: The author explains how to write the algebraic expression as a trigonometric function of theta .

Concept explainers

Videos

To write: The algebraic expression as a trigonometric function of θ, where 0<θ<π2 by using the trigonometric substitution. x2−16,x=4secθ

Want to see the full answer?

Chapter 5 Solutions

The algebraic expression as a trigonometric function of θ , where 0 < θ < π 2 by using the trigonometric substitution. x 2 − 16 , x = 4 sec θ

To write:

The algebraic expression as a trigonometric function of θ, where 0<θ<π2 by using the trigonometric substitution.

x2−16,x=4secθ