Find Where Y=cosx is Decreasing: -π to π

  • Thread starter rocomath
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In summary, the conversation involved discussing a problem related to the function y=cos x and determining the range of x values for which the function is decreasing. The correct answer is (0, pi), but the book's answer is incorrect as it states -3pi/2 < x < 3pi/2, which is not in the given interval of [-pi, pi]. The conversation then moves on to discussing a different question, and it is noted that the book's answer may be incorrect due to the use of "new math."
  • #1
rocomath
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Hmm ... I did this problem for a friend.

From what x values is [tex]y=cos x[/tex] decreasing from [tex]-\pi\leq x\leq\pi[/tex]

http://img440.imageshack.us/img440/3876/baocu5.jpg​
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*it should be [tex]-\frac{\pi}{2} \ \mbox{not} \ -\frac{3\pi}{2}[/tex]

It's decreasing from [tex](0,\pi)[/tex] but the answer she gave me from the back of the book is [tex]-\frac{3\pi}{2}<x<\frac{3\pi}{2}[/tex]
 
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  • #2
Nvm ... we apparently moved onto a different question, lol.
 
  • #3
The book's wrong
 
  • #4
Must be some of that new math :confused:
 
  • #5
Feldoh said:
The book's wrong
LOL, no she started asking about a different question ... I just didn't realize, ha. I was like wtf ... b/c the answer she gave me wasn't even in the interval they were asking about! haha, I kept saying no it's wrong! And I'll prove it by asking the PF Gods :)
 
  • #6
It looks a bit weird when it askes for the answer on the interval [-pi,pi] the books gives the answer as [-1.5pi,1.5pi]
 

1. What does it mean for a function to be decreasing?

Decreasing means that as the input values increase, the output values of the function decrease. In other words, the function is getting smaller as the input values get larger.

2. How do you find where y=cosx is decreasing?

To find where y=cosx is decreasing, we need to look for the intervals on the x-axis where the slope of the function is negative. This can be done by finding the critical points and analyzing the sign of the derivative of the function.

3. What is the domain of the function y=cosx?

The domain of the function y=cosx is all real numbers. In other words, there are no restrictions on the input values for this function.

4. Can y=cosx be decreasing for values outside of the interval -π to π?

No, the function y=cosx is only defined for values between -π and π. Therefore, it can only be decreasing within this interval.

5. How many times does y=cosx decrease within the interval -π to π?

The function y=cosx has infinite decrease within the interval -π to π. This is because the function is continuously decreasing as the input values increase.

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