In Exercises 29–44, graph two periods of the given cosecant or secant function.
y = csc(x − π)
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
7m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Cosecant Function
The cosecant function, denoted as csc(x), is the reciprocal of the sine function. It is defined as csc(x) = 1/sin(x). The cosecant function is undefined wherever the sine function is zero, leading to vertical asymptotes in its graph. Understanding the properties of the sine function is crucial for accurately graphing the cosecant function.
Periodic functions repeat their values in regular intervals, known as periods. For the cosecant function, the period is 2π, meaning the function's values repeat every 2π units along the x-axis. When graphing, it is essential to identify key points, such as the locations of asymptotes and maximum or minimum values, to accurately represent the function over its period.
A phase shift occurs when a function is horizontally shifted along the x-axis. In the function y = csc(x − π), the phase shift is π units to the right. This shift affects the location of the function's key features, such as its asymptotes and peaks, and is important for accurately graphing the function in relation to its standard position.