Question 971803: For the equation
cos(5 x) = −1
find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π.
2dp
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For the equation
cos(5 x) = −1
find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π.
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cos(5x)=-1
5x=π
x=π/5
There is only one solution in the given interval.
Answer by ikleyn(53909)  (Show Source):
You can put this solution on YOUR website! .
For the equation
cos(5 x) = −1
find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π.
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Regarding this problem, I'd like to make two comments.
First, in Math text, a professional Math writer would never write for such problem 0 <= x <= 2π.
A professional writer will write 0 <= x < 2π. Find the difference.
Second, the solution and the answer in the post by @lwsshak3 are incorrect.
For correct solution, see my post below.
cos(5x) = -1
5x = π, 3π, 5π, 7π, 9π, . . .
x =  ,  ,  = π,  ,  , . . .
For greater or smaller values of 5x, values of x will be out of the given interval.
So, there are 5 solutions to the given equation in interval 0 <= x < 2π.
The smallest is . The greatest is . The number of solutions is 5. ANSWER
Solved correctly.
I am surprising to see so elementary error in the post by @lwsshak3.
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