# Graph analysis with trig involved

• airportman92
In summary, the conversation discusses finding the roots, first and second derivatives, and inflection points of the equation y=sin2x-2sinx. The speaker has already found the roots and derivatives, but is unsure how to find the roots of the derivatives to determine minimums, maximums, and inflection points. They also question the existence of an inflection point and the differentiability and continuity of the original equation. They also ask about finding the domain and range. A suggestion is made to use the double angle formula to find the first derivative, and then solve for x to find the roots of the second derivative.
airportman92

## Homework Statement

given: y=sin2x-2sinx

## The Attempt at a Solution

i already found the roots of the equation, i also found the first and second derivatives which are 2cosx2-2cosx and -4sin2x+2sinx. however, i do not know how to find the roots for these equations in order to do mins and maxes and inflection pt. is it true that the inflection piont is zero, because that's how someone said to do it, but would that mean no concavity at all? and the original is differentiable and continuous correct? also, how wouuld i find the domain and range of this?

For the first derivative, use the double angle formula

cos2x=2cos2x-1 = 1-2sin2x

Solve for x and sub that into the expression for y''.

## 1. What is graph analysis with trig involved?

Graph analysis with trig involves using trigonometric functions, such as sine, cosine, and tangent, to analyze and interpret data represented in a graph. This type of analysis is commonly used in fields such as physics, engineering, and mathematics.

## 2. How do you use trigonometry to analyze graphs?

To use trigonometry to analyze graphs, you first need to identify the trigonometric function that represents the data on the graph. You can then use this function to calculate values such as amplitude, period, and frequency, which can provide insights into the behavior of the data.

## 3. What are some real-world applications of graph analysis with trig involved?

Graph analysis with trig has many real-world applications, including analyzing the motion of objects, predicting the behavior of waves, and modeling natural phenomena such as tides and sound waves. It is also used in fields such as surveying, navigation, and astronomy.

## 4. What are the benefits of using trigonometry in graph analysis?

Trigonometry allows for a more precise and accurate analysis of data represented in a graph. By using trigonometric functions, we can uncover patterns and relationships that may not be immediately apparent from the graph alone. It also allows for more complex and sophisticated analyses of data.

## 5. Are there any limitations to using trigonometry in graph analysis?

While trigonometry can be a powerful tool in graph analysis, it does have some limitations. It is often only applicable to data that follows a regular, predictable pattern, and may not work well with highly complex or irregular data. Additionally, it requires a solid understanding of trigonometric concepts and functions to use effectively.

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