Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

Taylor Series Expansion of Cosine and Sine

VIEWS: 221 PAGES: 2

									                                                                  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.

								
To top