Solve for x:

sin3x=1/2

Can someone please help me with this porblem? I'm not sure if my answers are right, but I obtained x=ð+12ðk/18 and x=5ð+12ðk/18.

sin(3x) = 1/2

3x = pi/6 + 2k*pi, 5pi/6 + 2k*pi
x = pi/18 + (2/3)k*pi, 5pi/6 + (2/3)k*pi

Thank you Marth!

To solve the equation sin(3x) = 1/2, we need to find the values of x that satisfy this equation. We can do this by examining the unit circle and using the properties of sine.

1. Start by finding the reference angle for 1/2: The reference angle for 1/2 is π/6 or 30°, as sin(π/6) = 1/2.

2. Since the period of sine is 2π, we can add integer multiples of 2π to the solutions. Let's call the integer multiple k.

3. To find the solutions for 3x, we need to find the angles whose sines are 1/2. These angles occur in the first and second quadrants.

In the first quadrant:
- The angle whose sin is 1/2 is π/6 (30°).
- The angle 3x will be π/6, and we need to add 2πk to account for the period. So one solution is π/6 + 2πk.

In the second quadrant:
- The angle whose sin is 1/2 is 5π/6 (150°).
- The angle 3x will be 5π/6, and we need to add 2πk to account for the period. So another solution is 5π/6 + 2πk.

4. Now we can solve for x by dividing both sides of those equations by 3:
- For the first solution: x = (π/6)/3 + (2πk)/3.
- For the second solution: x = (5π/6)/3 + (2πk)/3.

Simplifying these equations gives us:
- For the first solution: x = π/18 + (2πk)/3.
- For the second solution: x = 5π/18 + (2πk)/3.

So the correct solutions for x are x = π/18 + (2πk)/3 and x = 5π/18 + (2πk)/3.

It seems that your answers are not entirely correct. Make sure you divide the whole equation by 3 in order to obtain the correct solutions.