chapter3(1) - angle of elevation of the Sun The length of...

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MATH1010: Chapter 3 cont… 1 DIFFERENTIATION RULES cont … Derivatives of Trigonometric Functions (Section 3.4, pg. 211) In the past few lectures, we’ve introduced differentiation, and rules to help us take derivatives quickly, but what about trig functions…how do we differentiate them? Graphical Illustration: So, is x x dx d cos ) (sin = ??? Let’s check…first, we’ll need to know the following 2 limits: 1 sin lim 0 = θ 0 1 cos lim 0 =
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MATH1010: Chapter 3 cont… 2 And now, we proceed using the definition of a derivative (First Principles): Example: x x x x x f 10 cos 3 sin ) ( 5 + = Example: x x x x f cos sin 1 ) ( + + =
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MATH1010: Chapter 3 cont… 3 Example: Find ) (tan x dx d Derivatives of Trigonometric Functions x x dx d cos ) (sin = x x dx d sin ) (cos = x x dx d 2 sec ) (tan = x x dx d 2 csc ) (cot = x x x dx d tan sec ) (sec = x x x dx d cot csc ) (csc = Example: 1 sec 1 tan ) ( 2 + = x x x x f Application: On a sunny day, a 20 m tall flagpole casts a shadow that changes with the
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Unformatted text preview: angle of elevation of the Sun. The length of the shadow s is related to the angle of elevation of the Sun, θ , by the formula cot 20 = s . Find the rate at which the length of the shadow is changing with respect to when is 45 o . [Source: “Calculus: Early Transcendentals”, 8 th ed. by H. Anton, I. Bivens, and S. Davis, 2005] Finally, we can use the trig limits we introduced earlier to help us compute other trigonometric limits. Recall: 1 sin lim = → MATH1010: Chapter 3 cont… 4 Example: Find x x x ) 3 sin( lim → Example: Find ) 4 sin( ) 7 sin( lim x x x → Example: Find x x x 2 ) 5 tan( lim → Example: Find ) 8 tan( ) 9 sin( lim x x x →...
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chapter3(1) - angle of elevation of the Sun The length of...

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