The equation:
sin(5x) = 1/2
Has 10 solutions on the interval [0, 2pi].
How many solutions are in the given interval?
Here we have the equation:
sin(5x) = 1/2
And we want to know how many solutions are on the interval [0, 2pi].
Notice that, for the general sine equation:
sin(x)
There are two values of x on the interval [0, 2pi] such that:
sin(x) = 1/2.
Then, if we add a factor 5 (this is a horizontal compression of scale factor 5).
Then the number of solutions should also be multiplied by 5.
So sin(5x) = 1/2 has:
2*5 = 10 solutions.
You also can check this on the graph, where the green line is:
y = sin(5x)
The blue line is:
y = 1/2
And as you can see, the two lines intersect 10 times on the given interval.
If you want to learn more about sine functions:
https://brainly.com/question/9565966
#SPJ1
