How to Find Minimum Value of Sine Curve Using Derivatives

[9giddjl]

Homework Statement

How do I calculate the min of a sine curve using derivatives? eg. y=sin(2pi/60)

Homework Equations

I know how to find the max - find the derivative of the sine equation and equal the derivative to zero.

The Attempt at a Solution

^

 

[hotcommodity]

Does your textbook have a table of derivatives for trig functions? I'd start there.

 

[Vid]

y=sin(2pi/60) is a horizontal line.

 

[Defennder]

Well, you already know how to find the max. But the method you outlined doesn't just work for max, it works for min as well. Take sin x for example, differentiating sin x gives cos x. Setting cos x = 0 and solving for x gives pi/2 and 3pi/2 (if you restrict your answer to the interval of the initial period of the sine curve). One of this is min and the other is max. You'll know which is min and which is max by taking these 2 values, substituting them into the original sin x function and seeing which is greater. The greater one is the max value, the other one is the min value.

 

[Crazy Tosser]

Both the relative maximum and relative minimum have a slope, and, thus, derivative of zero. A useful thing is to find the zero's of the derivative graph, and make a sign chart. When a function stops increasing, and starts decreasing - you know it's the maximum (derivative switches from positive to negative). When the function stops decreasing and starts increasing - you know its the rel. minimum (derivative changes from negative to positive). Also, ALWAYS check at the endpoints, if you have an interval for your function. Also, remember that in periodic functions there are a lot of maximums and minimums, so when you write the x-values of them, make them periodic also, like $$\frac{\pi}{2}+\pi x$$, or something like that.

Hope I didn't confuse you too much.

 

[HallsofIvy]

Homework Statement

How do I calculate the min of a sine curve using derivatives? eg. y=sin(2pi/60)

Homework Equations

I know how to find the max - find the derivative of the sine equation and equal the derivative to zero.

The Attempt at a Solution

^

As Vid said. "y= sin(2pi/60)" is not a FUNCTION of x, but a constant. Its graph is a straight line and its minimum value is its constant value, sin(2pi/60). Are you sure there was not an x in the formula?