Critical Points of a trig function

• realism877
In summary, The conversation discusses the critical points of a trigonometric function, which are found to be (pi), (pi/3), and (5pi/3). The first derivative of the function is also mentioned, and it is differentiated into -sin(x)+2sin(2x). The conversation also explores a possible solution to the function using the zero product property. It is concluded that the critical points are not correct, and pi/2 is suggested to be a point instead of pi. The derivative is then clarified to be sin2x-sinx.
realism877
Trig function:-sinx+(1/2)sin2x(2)

The criticial points are (pi), (pi/3), and (5pi/3).

Am I correct?

Is that the first derivative there, or is it not differentiated?
$$-sin(x)+2sin(2x)$$

Yes, the first derivative.

Well,
Given that $sin(2x) = 2sin(x)cos(x)$, you could say the following:
$4sin(x)cos(x)-sin(x)=0$
$sin(x)(4cos(x)-1)=0$
Using the zero product property, what are the solutions to that?

I just want to know if my critical points are correct or not.

No, they are not

Is pi/2 a point instead of pi?

I'm sorry.

The derivative is sin2x-sinx

realism877 said:
I'm sorry.

The derivative is sin2x-sinx

In that case you were right.

What are critical points of a trig function?

Critical points of a trig function are points where the function's derivative is equal to zero. These points are important because they can help determine the maximum and minimum values of the function, as well as any potential inflection points.

How do you find critical points of a trig function?

To find critical points of a trig function, you need to take the derivative of the function and set it equal to zero. Then, solve for the variable to find the x-values of the critical points. You can also use a graphing calculator or software to plot the function and locate the critical points.

Why are critical points important in trigonometry?

Critical points are important in trigonometry because they help determine the behavior and shape of a trig function. They can also help in solving optimization problems, where the goal is to find the maximum or minimum value of a function.

Can a trig function have more than one critical point?

Yes, a trig function can have multiple critical points. Depending on the complexity of the function, there can be an infinite number of critical points. It is important to consider all critical points when analyzing the behavior of a trig function.

How can critical points be used to analyze a trig function?

Critical points can be used to analyze a trig function by determining the maximum and minimum values of the function, as well as any potential inflection points. This information can help in understanding the behavior and shape of the function, and can also be useful in solving real-world problems involving trigonometry.

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