How do you graph #y = -cos ( x- pi/4)#?

Question

Victoria Adebayo · Accepted Answer

You can extract various information only by looking at your function:
1] It is a cosine;
2] the #-1# in front of it tells us that the amplitude is #1# and every time we evaluate the #cos# we have to change sign;
3] The #1# in front of #x# tells us that the period is #1=(2pi)/(period)#
and #period=2pi#;
4] #-pi/4# is the starting angle or initial phase that is the angle when #x=0#;

Madelyn Adams · Answer

undefined To graph $ y = -\cos(x - \frac{\pi}{4}) $, follow these steps:

1. Identify the key components: The function $ y = -\cos(x - \frac{\pi}{4}) $ is a cosine function with a horizontal shift of $ \frac{\pi}{4} $ units to the right and a reflection about the x-axis due to the negative sign.

2. Determine the period: The period of a cosine function is $ 2\pi $.

3. Find the critical points: The critical points occur when $ \cos(x - \frac{\pi}{4}) = 0 $. This happens at $ x = \frac{\pi}{4} + k\pi $, where $ k $ is an integer.

4. Plot the critical points: The critical points occur at $ x = \frac{\pi}{4}, \frac{\pi}{4} + \pi, \frac{\pi}{4} + 2\pi, \ldots $.

5. Sketch the graph: Using the key components and critical points, sketch the graph of $ y = -\cos(x - \frac{\pi}{4}) $.

6. Repeat the pattern: Since cosine is a periodic function, the graph will repeat every $ 2\pi $ units.