For each function, give the amplitude, period, vertical translation, and phase shift, as applicable. y = cot (x/2 + 3π/4)
Verified step by step guidance
1
Identify the standard form of the cotangent function: .
Determine the amplitude: For cotangent functions, amplitude is not defined as they do not have maximum or minimum values.
Find the period: The period of is . Here, , so the period is .
Determine the phase shift: The phase shift is given by . Here, and , so the phase shift is .
Identify the vertical translation: The vertical translation is given by . In this function, , so there is no vertical translation.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
0m:0s
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Amplitude
Amplitude refers to the maximum distance a wave reaches from its central axis or equilibrium position. In trigonometric functions like sine and cosine, amplitude is a key feature, but for functions like cotangent, which do not oscillate above and below a central line, amplitude is not defined. Understanding amplitude is crucial for analyzing periodic functions.
The period of a trigonometric function is the length of one complete cycle of the wave. For the cotangent function, the standard period is π, but it can be altered by a coefficient in front of the variable. In the given function y = cot(x/2 + 3π/4), the period is determined by the coefficient of x, which in this case is 1/2, resulting in a period of 2π.
Phase shift refers to the horizontal displacement of a periodic function along the x-axis. It is determined by the constant added or subtracted from the variable inside the function. In the function y = cot(x/2 + 3π/4), the phase shift can be calculated by setting the inside of the cotangent function equal to zero, leading to a shift of -3π/4 to the left, which affects the function's starting point.