# Trigonometry and derivative

• Apr 28th 2006, 12:31 PM
totalnewbie
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 ?
• Apr 28th 2006, 12:52 PM
CaptainBlack
Quote:

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
• Apr 29th 2006, 06:03 AM
CaptainBlack
Quote:

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

RonL
• Apr 29th 2006, 07:21 AM
totalnewbie
Quote:

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

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.
• Apr 29th 2006, 08:02 AM
CaptainBlack
Quote:

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