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Name: _______________________ Date: ___________ Taylor Series Expansion of Cosine and Sine The sine and cosine function and other trigonometric functions can be expressed as a series that continues until infinity. Note: x in the series below is expressed in radians, not degrees. 1. Research radians and how to convert degrees to radians and vice versa. 2. Use the series below to calculate the sine and cosine for the following angles: a. 20o b. 30o c. 45o d. 60o e. 75o x 3 x 5 x 7 x 9 x11 sin x x .... 3! 5! 7! 9! 11! x 2 x 4 x 6 x 8 x10 cos x 1 .... 2! 4! 6! 8! 10! 3. How effective are these series at yielding the same result as your calculator? 4. How many terms in each equation would give a sufficient approximation for the sine and cosine? Rubric – Taylor Series Expansion of Cosine and Sine Level 1 Level 2 Level 3 Level 4 Researching radians Incomplete Reasonable, though Explanation regarding Detailed and explanation of radians not complete, radians and how to complete explanation and how to convert. explanation about convert is present. of radians and how to radians and how to convert degrees to convert. radians and vice versa. Calculations of Few calculations Shows some Shows correct Shows correct radians shown. calculations. calculations. calculations. Series Calculations Series used with Series used with a Series correctly used, Series used correctly several errors. few errors. showing most steps in showing all the steps the calculations. in the calculations. Answers to Questions Identifies few Identifies some Identifies most Detailed and arguments for the arguments for the arguments for the complete description effectiveness of the effectiveness of the effectiveness of the of effectiveness of series. series. series. series. Mainly incorrect Forms an incomplete Identifies a minimum Identifies the correct conclusion on the conclusion on the number of terms minimum number of minimum number of minimum number of necessary to make a terms to make a terms. terms. sufficient sufficient approximation. approximation.
"Taylor Series Expansion of Cosine and Sine"