# Complete cycle of a trig function.

• chay722
In summary, a complete cycle of a trigonometric function refers to one full repetition of the function's graph, including the maximum and minimum values, x-intercepts, and period. The number of degrees or radians in a complete cycle depends on the specific function, and it can be used to solve equations by identifying key features of the graph. The starting point of a complete cycle can vary without affecting the overall shape of the graph.
chay722
Hi, I have an assignment where I must graph various trig functions and the instructions say to graph each for a complete cycle. Does a complete cycle mean until the graph begins to repeat so for instance a complete cycle for a sin graph would be from the range 0 to 2 pi? Thanks for any help.

Yes. x=0 to 2 pi makes a complete cycle of sin(x).

K. thank you very much,

## 1. What is a complete cycle of a trig function?

A complete cycle of a trigonometric function refers to one full repetition of the function's graph. This means starting at one point on the graph, the function will go through all of its possible values and return to the starting point.

## 2. What are the key features of a complete cycle of a trig function?

The key features of a complete cycle of a trigonometric function are the maximum and minimum values, the x-intercepts, and the period. The maximum and minimum values represent the highest and lowest points on the graph, while the x-intercepts are where the function crosses the x-axis. The period is the distance between two consecutive repetitions of the function.

## 3. How many degrees or radians are in a complete cycle of a trig function?

The number of degrees or radians in a complete cycle of a trigonometric function depends on the specific function being used. For example, the sine and cosine functions have a period of 360 degrees or 2π radians, while the tangent function has a period of 180 degrees or π radians.

## 4. How can the complete cycle of a trig function be used to solve equations?

The complete cycle of a trigonometric function can be used to solve equations by identifying key features of the graph, such as the x-intercepts, and using them to find the solutions. This is commonly done by setting the function equal to a value and using the periodic nature of the function to find all possible solutions.

## 5. Can the complete cycle of a trig function have different starting points?

Yes, the complete cycle of a trigonometric function can have different starting points. This is because the function is periodic, meaning it repeats itself at regular intervals. As long as the function follows the same pattern, it can have different starting points without affecting the overall shape of the graph.

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