Graphing y=cos^2(x) - Trig Graphs

In summary, the conversation is about a recent trigonometry test where the speaker found the material easy except for one problem involving graphing a function. The function was y=cos^2(x) and the speaker graphed it by squaring each cosine value. However, their teacher only counted it as half correct and suggested that changing the equation to y=(1+cos2x)/2 would have been the correct approach. The speaker realized their mistake and ended up with an A on the test.
  • #1
tycon69
18
0
We had a test recently in trig on graphing trig functions. I found it all quite simple except a problem that we had not discussed. I believe the problem was something like y=cos^2(x). I graphed it by squaring each cosine value, because i had no idea what else to do, but when i turned the test in, my teacher told me that it was only half correct. I ended up with a nice M (maybe W) shape. Thinking back, would it have been correct to change the equation to y=(1+cos2x)/2 and then graph it?
 
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  • #2
tycon69, what are you trying to express? Are you asking about [cos(x)]*[cos(x)], or what? You seem to mean just that. All the values will be positive (the 'y' values). The 'M' shape that your teacher indicated. The amplitude is 1.
 
  • #3
Maybe you took the squares of negative cosines as negative? cos^2(x) is greater than 0 everywhere, was your graph?
 
  • #4
yes it was, it's amplitude was one and everything was above 0. I just graphed it on a graphing application and the graph is identical to what i graphed. I must have overlooked a simple mistake, i'll have to look at it monday. Luckily she only counted off half so i ended up with an A. Thx for trying to help me, i know my explanation was quite confusing.
 
  • #5
tycon69 said:
We had a test recently in trig on graphing trig functions. I found it all quite simple except a problem that we had not discussed. I believe the problem was something like y=cos^2(x). I graphed it by squaring each cosine value, because i had no idea what else to do, but when i turned the test in, my teacher told me that it was only half correct. I ended up with a nice M (maybe W) shape. Thinking back, would it have been correct to change the equation to y=(1+cos2x)/2 and then graph it?
What was the problem? Just to graph the function?
 
  • #6
Yes, the problem was just to graph the function. I found out it was a pretty stupid mistake on my part in that i graphed cos(0)=0 when it should have of course been 1:bugeye:
 

1. What is the basic shape of the graph of y = cos^2(x)?

The basic shape of the graph of y = cos^2(x) is a periodic function that oscillates between 0 and 1, with a period of 2π.

2. How do I find the amplitude of y = cos^2(x)?

The amplitude of y = cos^2(x) is 1, as the function oscillates between 0 and 1. This means that the maximum value of the function is 1 and the minimum value is 0.

3. What is the period of y = cos^2(x)?

The period of y = cos^2(x) is 2π, which is the distance between two consecutive peaks or troughs of the graph.

4. How do I find the x-intercepts of the graph of y = cos^2(x)?

The x-intercepts of y = cos^2(x) occur at every multiple of π, as the function crosses the x-axis at these points. This is because cos^2(x) = 0 when x is equal to any odd multiple of π.

5. How can I use transformations to graph y = cos^2(x)?

To graph y = cos^2(x), you can apply transformations to the basic cosine function. For example, adding a constant to the function will cause a vertical shift, multiplying by a constant will cause a vertical stretch or compression, and changing the sign of the function will cause a reflection over the x-axis.

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