Secondary V • 9mo.
how do i solve this equation:
find the smallest positive number for 3sin(2x-6)=1
the correct answer is 0.028328455
how do i solve this equation:
find the smallest positive number for 3sin(2x-6)=1
the correct answer is 0.028328455
Explanation from Alloprof
This Explanation was submitted by a member of the Alloprof team.
Hi there!
Thank you for reaching out :
We'll start with the given equation and isolate the sine function:
3sin(2x-6) = 1
sin(2x-6) = 1/3
To isolate the x, we need to use arcsine (or sin-1).
2x-6 = arcsin (1/3)
2x = arcsin(1/3) + 6
x = (arcsin(1/3) + 6) / 2
We can now find the value of x. However, that may not be your answer; since the sine function has a period of 2π, there are infinite solutions for x. To find the smallest value possible, we have to add multiples of the period 2π to x until we get a value in the range [0, 2π].
x ≈ 3.01416 radians
x + 2π ≈ 3.01416 + 2π ≈ 9.15585 radians (This is greater than 2π)
x + 4π ≈ 3.01416 + 4π ≈ 15.2975 radians (This is greater than 2π)
There may be a small error in the answer you provided us. You could always go over this problem with your teacher so that they can correct the answer if needed!
To learn more about the sine function, click on that link:
Hope that helped!
Have a wonderful day,
Ariane