At 01:09 PM 3/30/99 EST, CoolMath2@AOL.COM wrote:
>In a message dated 3/29/99 4:45:25 PM Pacific Standard Time,
>jcotten@mars.sunyjcc.edu writes:
>
><< I agree with you, the students I have seen struggle with Calculus are
>really
> having algebra problems and not caclulus problems. >>
>
>I see more problems with their knowledge of trig. Especially when their trig
>teacher has not required them to memorize the unit circle and identities. The
>famous mistake:
>
>sin(5x) = 5sinx.... SURE!! Factoring the 5 out *does* make those limit
>problems a lot easier!
I see their biggest problem being the lack of understanding and familiarity
with log and exponential functions. How many weeks do we spend teaching
trig vs. exp and log functions.
On a more general note, I agree that sin(5x) = 5sin(x) is a common problem.
I think that is more due to a general lack of understanding that sin(x) is a
function, just like f(x).
As for "memorizing the unit circle" I disagree. The only trig funciton I
have memorized is sin(0) = 0 and that is only because I have used it so much
I have memorized it in spite of my attempts not to. I tell my students,
"All I know about trig is 'Sine is the y reading; tells you how far you are
from the x-axis. Cosine is the x reading; tells you how far you are from
the y-axis." If you ask me to find the sin (150 degrees) I quickly draw a
unit circle (in my head) and note that sine is the "short distance" so it is
1/2 and it is in the positive direction from the x-axis, hence the sin 150
degrees is +1/2. (That whole process takes about 2 to 3 seconds.)
I still don't know the Pythagorean Identities using tangent and secant, or
cotangent and cosecant. I know "sine squared plus cosine squared = one" and
it only takes about 3 seconds to divide by sine or cosine as needed and get
the appropriate formula.
I guess I'm just weird. :-)
>
>Karen
>Orange Coast College
>www.coolmath.com
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