Question

Y=2cos2x-3

Answer 1

y=2cos^x-sin^x -3

Answer 2

The expression Y = 2cos(2x) - 3 represents a function in terms of the trigonometric cosine function, where Y is the dependent variable and x is the independent variable.

Here's how you can interpret and work with this function:

1. Amplitude: The coefficient of the cosine term, which is 2, represents the amplitude of the function. In this case, the amplitude is 2, meaning the graph of this function will oscillate between 2 and -2.

2. Frequency: The argument of the cosine function, which is 2x, determines the frequency of the oscillation. In this case, the frequency is twice that of a regular cosine function.

3. Phase Shift: There is no phase shift (horizontal shift) indicated in this expression because there is no term like cos(2x - θ). The phase shift is 0.

4. Vertical Shift: The constant term, which is -3, indicates a vertical shift. In this case, the graph is shifted downward by 3 units.

If you want to graph this function, you can choose a range of values for x, calculate the corresponding Y values, and then plot the points to see the graph of the function. The graph will be a cosine wave with an amplitude of 2, a frequency of 2, and shifted down by 3 units.