How to draw graph of y=2cos(x+60).
I would suggest using "desmos" free on line graphing program and just graphing
1) cosx
then
2) 2cosx
then
3) 2cos(x+60)
because that way you will see the change in the amplitude and phase shift : )
Wolfram, one of the better apps for math, makes it quite easy
to follow Ms Pi's suggestion
https://www.wolframalpha.com/input/?i=plot+y+%3D+cosx%2C+y+%3D+2cosx%2C+y+%3D+2cos%28x%2B%CF%80%2F3%29
To draw the graph of the function y = 2cos(x + 60), you can follow these steps:
1. Determine the amplitude: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the coefficient is 2, so the amplitude is 2.
2. Determine the period: The period of a cosine function is the horizontal length of one complete cycle. The standard period of a cosine function is 2π. In this case, the coefficient in the argument of the cosine term is 1, so the equation is x + 60 = 2π. Solving for x gives x = 2π - 60. Therefore, the period is 2π.
3. Determine the phase shift: The phase shift of a cosine function is the horizontal shift of the graph. In this case, the argument of the cosine function is x + 60, which means the graph is shifted 60 units to the left.
4. Find the x-intercepts: To find the x-intercepts, set y to zero and solve for x. In this case, set y = 2cos(x + 60) equal to zero. This means that cos(x + 60) = 0. Solving for x gives x = -60° and x = 120°.
5. Sketch the graph:
- Start by plotting the x-intercepts at (-60°, 0) and (120°, 0).
- Since the amplitude is 2, the highest point on the graph will be 2 units above the x-axis, and the lowest point will be 2 units below the x-axis.
- As the period is 2π, you can divide the x-axis into equal intervals of 2π. Each interval represents one complete cycle of the function.
- The phase shift is -60°, so shift the graph 60° to the left.
- Plot a few points on the graph by evaluating y = 2cos(x + 60) at various values of x within one interval. Connect these points smoothly to form a curve.
By following these steps, you can successfully draw the graph of y = 2cos(x + 60).