Here is a group activity I use to work on the misconception that 1/2 sin
(2x) = sin x.
On a unit circle, draw and label an angle, A, in standard position. Have
the students draw the angle 2A on the same unit circle. Using the circular
definitions of the trig functions, have them estimate sin A, cos A, sin 2A,
and cos 2A and calculate 1/2 sin(2a), 1/2 cos (2A), 2 sin A and 2 cos A from
their estimations. (Have them fill in the blanks to answer these
questions.) Follow up with a series of true/false, justify your answer
questions like:
T F sin (2A) = 2 sin A
T F cos (2A) = 2 cos A
T F sin A = 1/2 sin (2A)
T F cos A = 1/2 cos (2A)
T F If pi/2 < A < pi, then cos A >0
Ask these same questions for about 8 drawings of circles with positive and
negative angles in all of the quadrants, then ask the students to identify
which statements seem to be in general true and which ones are clearly
false.
Martha
-----Original Message-----
From: Tischer, Diane <DTISCHER@metropo.mccneb.edu>
To: 'mathedcc@archives.math.utk.edu.' <mathedcc@archives.math.utk.edu>
Cc: Tischer, Diane <DTISCHER@metropo.mccneb.edu>
Date: Thursday, March 18, 1999 9:36 AM
Subject: [MATHEDCC] Technology and Trig
>I am working on using technology to address the misconceptions that I fight
>most frequently with students in a trigonometry course. I am hoping that
>there are materials somewhere that have already dealt with the issues. If
>anyone knows of software, web sites, etc. that might be possibilities,
>please let me know. The issues I am focusing on deal with errors in
>interpreting notation and are:(The e-mail editor I am using does not allow
>me to add superscripts and type nicely so I hope that these are
>understandable.)
> 1. sin(superscript -1)x does not mean csc x even though
>sin(superscript 2)x means sin squared of x.
> 2. The statement: sin(superscript -1)x = theta should be translated
>to sin theta = x.
>and 3. When simplifying product to sum answers, realize that 1/2(sin 4x
>+ sin 2x) does NOT equal sin 2x + sin x. (I have just completed graphing
y
>= 1/2(sinx) and y = sin 2x and they do that successfully but don't relate
>it to this!)
>
>Any suggestions would be helpful and appreciated!
>Diane Tischer
>Mathematics Department
>Metropolitan Community College
>Box 3777
>Omaha, NE 68103
>(402) 457-2504
>
>dtischer@metropo.mccneb.edu
>***************************************************************************
*
>* To post to the list: email mathedcc@archives.math.utk.edu *
>* To unsubscribe, send mail to: majordomo@archives.math.utk.edu
*
>* In the mail message, enter ONLY the words: unsubscribe mathedcc
*
>* Words in the Subject: line are NOT processed! *
>* Archives at http://archives.math.utk.edu/hypermail/mathedcc/
*
>***************************************************************************
*
>
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************