3.3 Derivatives of trigonometric Functions

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Before starting this section, you might need to review the trigonometric functions.

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10 Terms

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F(x)= sin x

If we sketch the graph of the function f (x)= sin x and use the interpretation of

f’ (x) as the slope of the tangent to the sine curve in order to sketch the graph of f9

<p>If we sketch the graph of the function f (x)= sin x and use the interpretation of</p><p> f’ (x) as the slope of the tangent to the sine curve in order to sketch the graph of f9</p>
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Geometric proof of the fundamental trigonometric limit

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Derivative of ( sin x )

cos x

<p>cos x </p>
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What is the derivative of (cos x)  ?

-sin x

<p>-sin x </p>
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What is the derivative of ( tan x ) ?

sec ² x

<p>sec ² x</p>
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What is the derivative of (csc x) ?

-csc x cot x

<p>-csc x cot x </p>
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What is the derivative of ( sec x )?

sec x tan x

<p>sec x tan x</p>
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What is the derivative of (cot x) ?

- csc ² x

<p>- csc ² x</p>
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Derivatives of Trigonometric Functions

Trigonometric functions are often used in modeling real-world phenomena. In particular, vibrations, waves, elastic motions, and other quantities that vary in a periodic manner can be described using trigonometric functions.

<p>Trigonometric functions are often used in modeling real-world phenomena. In particular, vibrations, waves, elastic motions, and other quantities that vary in a periodic manner can be described using trigonometric functions.</p>