Sketch the graph of the function. (Include two full periods.) y=2 cot(x+(π)/(2))

Name: Problem 38, Chapter 4: Precalculus
Uploaded: 2021-05-17T08:05:28-08:00
Duration: 3 min 10 s
Channel: Aman Gupta
Description: Sketch the graph of the function. (Include two full periods.) y=2 cot(x+(π)/(2))

step 1 In this problem, to get the graph of y equals to 2 cot x plus pi by 2, we will first get the two

Sketch the graph of the function. (Include two full...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Periodicity

Periodicity refers to the property of a function to repeat its values in regular intervals, called periods. For the cotangent function, this period is ?, which means the graph repeats its pattern every ? units along the x-axis. Understanding this is key when sketching multiple periods of the function.

Cotangent Function

The cotangent function is one of the primary trigonometric functions defined as the ratio of the cosine to the sine of an angle. Its graph is characterized by a series of repeating segments with vertical asymptotes where the sine equals zero, and it typically exhibits a decreasing trend within each period.

Phase Shift

Phase shift is a horizontal translation of a trigonometric function along the x-axis. In the function y = 2 cot(x + ?/2), the expression (x + ?/2) indicates that the graph is shifted left by ?/2 units. Recognizing and implementing this shift is important when accurately sketching the graph.

Vertical Scaling

Vertical scaling affects the steepness of the graph by multiplying the function by a constant factor. In this case, multiplying the cotangent function by 2 stretches the graph vertically, making the peaks and valleys appear farther from the x-axis. This transformation changes the overall appearance of the graph without affecting its periodicity or the location of its asymptotes.

Transcript

Please give Ace some feedback