Derivative

[simplethinker]

I need to find the slope of the equation: 50-50cos(1.8x)

after plugging it into (f(x+h)-f(x))/h I got: lim h->0 50(cos(1.8x)-cos(1.8x+1.8h))/h

then: lim h->0 50(cos(1.8x)-cos(1.8x)cos(1.8h)+sin(1.8x)sin(1.8h))/h

lim h->0 50( sin(1.8x)sin(1.8h)/h + cos(x)(1-cos(1.8h))/h )

lim h->0 sin(1.8h)/h = 1.8 : lim h->0 1-cos(1.8h)/h = 0, so it's:
lim h->0 50(1.8sin(1.8x)+0)

take the limit and it's:
90sin(1.8x)

ive gone over the work 3 times and cant find anything wrong but when i punch it in and compare it to (f(x+.0001)-f(x))/.0001 they're way different

anyone have any ideas of what im doing wrong?

[alexrudd]

I used [2nd] [calc] dy/dx, 90sin(1.8x), and (Y1(2.0001)-Y1(2))/.0001 at x=2 and got about -39 for each. What did you get?

[simplethinker]

I got -50 for 90sin(1.8x) and 69 for (f(x+.0001)-f(x))/.0001

[simplethinker]

ok, nvm i got it
i was in deg instead of rad mode lol

[alexrudd]

I was going to suggest checking that, but then realized that both the calculations are in degree mode. Does anyone know why would it make a difference?

[simplethinker]

For some reason taking the limit of the difference quotient in degrees changes it. I'll ask my teacher tomorrow

[Fallen Ghost]

While looking at a sinusoidal (didn't check the spelling on this) graphing line of equation y=sin(x), being in radians mode will make the space between the peaks of the equation (peaks: y=1 and negative peaks y=-1) is about 5 (something over 4 and under 10) . But in Degree mode, the space between is 360. So when you do sin(5) in radians, it gives
-0.95892427466313846889315440615599, but in degree it will give 0.087155742747658173558064270837474.

I love using the windows calculator in decimal scientific mode (look the number of digits...)

[simplethinker]

The number between 4 and 10 is 6.28 (2*pi). In one rotation there are 360 degrees.
Radians are based on the unit circle, a circle of radius 1 with its center at the origin (equation= (x**2 + y**2)==1 ) the circumference of that circle is 2*pi*r, and since the radius is 1 the circumference is 2*pi. Radians are the arc length, or section of the circumference formed between a angle of n degrees and the x-axis.
You can convert from deg -> rads by multiplying the degrees by pi/180, and rad ->degs by multiplying the rads by180/pi
check this in a calc by pushing in sin(45) in deg mode and sin(pi/4) [45*pi/180==pi/4] in rad, you will get .707 or .5**.5

when calculating sin(5) in radian mode that's calculating sin(5 rads), and 5 radians is about 287 degrees. Punch in sin(287) in degree mode and you'll get what you got for sin(5 rad)

[DarkerLine]

[simplethinker]

Good point, I always forget the derivatives of sin() and cos() are affected by deg/rad even if you have the rads converted to degs