Solve for t if 0<t<2pi

Note: both are less than or equal to .
Please help!!
I am not sure what I should do.

Is it something like sin t = .5 or something?

e^-1 cost +sint(-e^-t)=0

Do you mean

e^-t cost + e^-t sint = 0?
If so, factor out the e^-t and you have

e^-t (cost - sint) = 0

e^-t is never 0, so that leaves

sint = cost
or
tant = 1

I think you can work with that, eh? Remember all four quadrants.

To solve for t where 0 < t < 2π, you can use a step-by-step process.

1. Start with the inequality given: 0 < t < 2π. This means that t is greater than 0 and less than 2π.

2. Since t is a variable in this case, the first step is to isolate it. To do this, you can subtract 0 from both sides of the inequality: 0 - 0 < t - 0 < 2π - 0.

This simplifies to: 0 < t < 2π.

Now, you have narrowed down the possible values of t.

3. The inequality 0 < t means that t must be greater than 0. So, the lower limit for t is 0.

4. The inequality t < 2π means that t must be less than 2π. So, the upper limit for t is 2π.

Therefore, the solution for t is: 0 < t < 2π.

In other words, t can take any value between 0 and 2π, exclusive.