To solve the equation sin(3x) cos(2x) = 0, we can use the fact that a product is equal to zero if at least one of the factors is zero. This means we need to set each factor to zero and solve.
1. **Setting sin(3x) to zero:**
We first solve the equation sin(3x) = 0. The sine function is zero at integer multiples of π:
3x = nπ where n is any integer.
This leads to:
x = nπ/3
2. **Setting cos(2x) to zero:**
Next, we solve the equation cos(2x) = 0. The cosine function is zero at the odd multiples of π/2:
2x = (2m + 1)π/2 where m is any integer.
This simplifies to:
x = (2m + 1)π/4
3. **Summary of Solutions:**
From both parts, we get the general solutions:
- x = nπ/3 for sin(3x) = 0
- x = (2m + 1)π/4 for cos(2x) = 0
These equations give us all the x-values where the original equation holds true. You can substitute different integer values for n and m to get specific solutions.