13 Trigonometric Function and their derivatives
A: In high school “Degree measure” were used to indicate the size of an
angle, for ex, .
But in Calculus “Radian measure” are used to indicate the size of an
angle, for ex,
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Trigonometric Functions and Their Derivatives, Summaries of Mathematics
A comprehensive overview of trigonometric functions and their derivatives. It covers the transition from degree measure to radian measure, introduces the basic trigonometric functions, and delves into the derivatives of these functions. Various examples and exercises to illustrate the concepts, including finding the derivatives of specific functions at given values. This resource would be particularly useful for students studying calculus, as it covers fundamental topics in the field of trigonometry and its applications in differentiation. The detailed explanations and step-by-step solutions make this document a valuable study aid for university-level mathematics courses.
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2023/2024
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13 Trigonometric Function and their derivatives
A: In high school “Degree measure” were used to indicate the size of an angle, for ex,. But in Calculus “Radian measure” are used to indicate the size of an angle, for ex,
Radian Measure For an angle , the ratio of the length of arc to the ratio of the circle is the same, regardless of the radius of the circle. Thus Radian measure of
13.2 Derivatives of Trigonometric Functions
We will use following identities:
Derivative of by using the definition of the derivative of a function
We know by the definition of the derivative of a function The derivative of is (Identiity for ) (Rearranging the terms and factorizing) Hence
C: Basic derivatives of trigonometric Functions
Ex 1: Find the derivatives of the following functions:
(using chain rule)
. .[. ]
i) (Product Rule) ii) If then (Chain Rule)
1..
- .
Ex 3: Find the derivative of each function at the specified value of 3.1 when ).() Thus ).() 3.2 when ).(). ) Thus