1. What is the Cosine Shift Equation?

The cosine shift equation \( y = \cos(x - c) \) represents a cosine function with a phase shift. The parameter \( c \) determines the horizontal displacement of the cosine wave along the x-axis.

2. How Does the Calculator Work?

The calculator uses the cosine shift equation:

Where:

• \( x \) — Input value in radians
• \( c \) — Phase shift value in radians
• \( y \) — Output cosine value

Explanation: The equation calculates the cosine of the difference between the input value and the phase shift parameter, producing a shifted cosine waveform.

3. Importance of Cosine Shift Calculation

Details: Phase shift calculations are essential in signal processing, wave analysis, electrical engineering, and physics for analyzing periodic functions and waveform transformations.

4. Using the Calculator

Tips: Enter the x value and phase shift (c) in radians. The calculator will compute the corresponding y value of the shifted cosine function.

5. Frequently Asked Questions (FAQ)

Q1: What is phase shift in cosine functions?
A: Phase shift refers to the horizontal displacement of a cosine wave along the x-axis, determined by the parameter c in the equation y = cos(x - c).

Q2: How does phase shift affect the cosine graph?
A: A positive phase shift moves the cosine wave to the right, while a negative phase shift moves it to the left along the x-axis.

Q3: What are the units for x and c values?
A: Both x and c values should be entered in radians for accurate trigonometric calculations.

Q4: Can I use degrees instead of radians?
A: While possible with conversion, the calculator is designed for radians. Convert degrees to radians first (radians = degrees × π/180) if needed.

Q5: What is the range of output values?
A: The cosine function outputs values between -1 and 1 inclusive, regardless of the phase shift applied.