Explanation Given: The function is sin 61 ° − sin 60 ° . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Consider the function f ( x ) = sin x . Differentiate the function with respect to x . f ′ ( x ) = cos x Find the value of sin 61 ° − sin 60 ° . Now, apply the linear approximation with a = 60 ° and Δ x = 1 ° . First, find the values of a and Δ x in radians. a = 60 ° = π 3 radians and Δ x = 1 ° = π 180 radians Use the formula: f ′ ( a )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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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Chapter 4.1, Problem 34E

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Find the value of sin61°−sin60° using linear approximation.

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Chapter 4.1, Problem 33E

Chapter 4.1, Problem 35E

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Chapter 4 Solutions

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Find the value of sin 61 ° − sin 60 ° using linear approximation.

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