Explanation Given information: Two trigonometric expression is given as sin π 12 and cos π 12 . Concepts used: Addition formula, 1. ) sin ( A − B ) = sin A cos B − cos A sin B 2. ) cos ( A − B ) = cos A cos B + sin A sin B Calculation: Let us first calculate the value of sin π 12 . sin π 12 = sin ( π 3 − π 4 ) ⇒ sin π 12 = sin π 3 cos π 4 − cos π 3 sin π 4 { Using sin ( A − B ) = sin A cos B − cos A sin B } ⇒ sin π 12 = 3 2 × 1 2 − 1 2 × 1 2 ⇒ sin π 12 = 3 2 2 − 1 2 2 ⇒ sin π 12 = 3 − 1 2 2 ⇒ sin π 12 = 2 ( 3 − 1 )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 1.4, Problem 34E

To determine

The value of sinπ12 and cosπ12.

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Chapter 1.4, Problem 33E

Chapter 1.4, Problem 35E

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Chapter 1 Solutions

Calculus: Early Transcendentals

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The value of sin π 12 and cos π 12 .

Solution Summary: The author calculates the value of mathrmsinpi, based on two trigonometric expressions.

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The value of sinπ12 and cosπ12.

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Chapter 1 Solutions