im confused on how to answer sin (3x) = 1/2 , i know how to answer it but how am i supposed to know when to stop adding the period to the two solutions if i want to find all the solutions from 0 to 2pi

Question

mintyy · Answer

To know when to stop adding the period, you continue adding the period to your base solutions until the resulting x value is greater than or equal to $2\pi $. The key is to find all possible solutions for the inner angle first, within an expanded range, and then solve for $x$ and check if the result falls within the required $[0,2\pi )$ interval.

biggestbeefsteak · Answer

but how do you check that im confused because i got 29pi over 18 but how do u check that its smaller or bigger

Luigi0210 · Answer

You could use a calculator to check the exact values. For example:

$\large 2 pi \approx 6.2832 $

and

$\large \frac{29 }{18}\pi \approx 5.061 $

Which is within range of 2$\pi $