Thread: Trigonometry and derivative

The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
I analyzed function f(x)=4*(sin(x))^2
f'=8*sin(x)*cos(x)
The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
Why does not the first derivative show it ?

Originally Posted by totalnewbie

The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
I analyzed function f(x)=4*(sin(x))^2
f'=8*sin(x)*cos(x)
The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
Why does not the first derivative show it ?

Examine f(x) again - it is decreasing at x=150 degrees.

RonL

Originally Posted by totalnewbie

The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
I analyzed function f(x)=4*(sin(x))^2
f'=8*sin(x)*cos(x)
The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
Why does not the first derivative show it ?

Also, avoid using degrees in this sort of problem, the derivatives of the trig
functions you are familiar with are for the functions with the argument in
radians.

RonL

Originally Posted by CaptainBlack

Also, avoid using degrees in this sort of problem, the derivatives of the trig
functions you are familiar with are for the functions with the argument in
radians.

RonL

It depends on DRG. I use DEG mode. If I used RAD mode, I would have to use radians.
Anyway the problem is solved.

Originally Posted by totalnewbie

It depends on DRG. I use DEG mode. If I used RAD mode, I would have to use radians.
Anyway the problem is solved.

The "units" of f' are they "per radian" or "per degree"?

You are setting yourself up to make mistakes is you mix up how
you are measuring angles.

In your equation "f(x)=4*(sin(x))^2" the x is almost always in
radians.

RonL

I'm going to poke my nose in and say in another way what CaptainBlack is trying to say:
You can certainly do your trig functions in DEGREE mode, but the Calculus formulas for the derivatives are done in RADIANS. So if you are using degrees to calculate your angles you have to introduce extra factors in the Calculus formulas to get the correct answers.

It is MUCH safer to use radians when doing Calculus.

-Dan