# Another Trigonometric Equation

1. Oct 17, 2009

### TrueStar

1. The problem statement, all variables and given/known data

Solve for t

sin3tcost+cos3tsint=-1/2

2. Relevant equations

Sum and Difference Identities

3. The attempt at a solution

I saw this problem the the sum identity sin($\alpha$+$$\beta$$) looked like the way to begin solving for t.

This condenses to sin(3t+t)= -1/2 which is sin(4t)= -1/2

I let 4t=x and now have sin x= -1/2

The answers for this are 7$\pi$/6+2$\pi$n and 11$\pi$+2$\pi$n.

This means that 4t equals both 7$\pi$/6+2$\pi$n and 11$\pi$+2$\pi$n. I need to divide the four out to get t by itself.

The general solutions (I think) are t=7$\pi$/24+$\pi$n/2 and 11$\pi$/6+$\pi$n/2.

Did I miss anything or does this look correct?

Thanks!

2. Oct 17, 2009

### Staff: Mentor

In the next couple of lines, the 2nd expression should be 11$\pi$/6 +2$\pi$n, which it appears you caught later.
In the next line, you got the "divided by 6" back in the second expression, but forgot to divide by 4.
Make the above t=7$\pi$/24+$\pi$n/2 and 11$\pi$/24+$\pi$n/2.

3. Oct 17, 2009

### TrueStar

You're right. I had that written on my paper, but it's a typo here on the board. Thank you for reading my post!