Is anybody good with Maple?

[JayTee]

Is there an easy way to define a sine wave with a maximum slope of 80 degrees to the horizontal? This may just be a math question.

[Fels krone]

Maximum slope of 80 degrees?

Not sure what you mean there. I used maple a while ago; and for basic stuff like defining a sine wave, it seemed user friendly enough to figure out. Im guessing there should be a help section; the one in matlab is pretty useful.

[Siegmund]

Well, yes.

y = sin ax has derivative a sin ax, and steepest slope a.

Set a = arcsin(80 degrees.)

[Borodog]

I'm fairly certain that the derivative of sin(ax) wrt to x is not asin(ax).

[Fels krone]

derivative of sin(ax) is a*cos(ax)

Still dont understand what you mean by slope of 80 degrees. Amplitude, frequency, and phase are characteristics of a sine wave. If you wanted a sloped sine wave,
y = mx + a*sin(x).

[thylacine]

[ QUOTE ]
I'm fairly certain that the derivative of sin(ax) wrt to x is not asin(ax).

[/ QUOTE ]

FWIW I think this wrong answer is not as wrong as cos(ax).

[Jiggymike]

There's not much to it, I just dump that stuff all over my pancakes.

[Duke]

[ QUOTE ]
derivative of sin(ax) is a*cos(ax)

Still dont understand what you mean by slope of 80 degrees. Amplitude, frequency, and phase are characteristics of a sine wave. If you wanted a sloped sine wave,
y = mx + a*sin(x).

[/ QUOTE ]

I think I can describe what he means, unless he confused me, too.

Think of the sin wave as a line. At every point on that line you could find the slope. He's saying that he doesn't want the slope of the actual sin wave (which is a normal one left to right) to ever be above 80.

At some point in time the slope of that line will have a maximum value. If it were an extremely high frequency and amplitude, it would be close to 90 degrees. If it had an extremely low frequency it would be closer to 0. If sin waves inflected through the vertical it would be 90 degrees. They don't, and he just wants it to "max out" at 80.

[Neuge]

Your sine wave, "y = a sin(bx)", is subject to the constraint "ab cos(bx) < tan(80)".

Don't ask me to do that in Maple however, I've never used it.

EDIT: Changed ">" to "<".

[JayTee]

Thanks guys

This is my first experience with a CAS. I figured out what I had to do, but I had to work out the function on my own. I was trying to find out if there was a way to define a cosine wave over a specific interval with a slope +/- tan(80) at its center and a limited amplitude and be continuous with a piecewise function.

I haven't studied much higher math, so I pretty much had to figure out a method on my own.