Solve each equation for x, where x is restricted to the given interval.

y = 1/2 cot 3 x , for x in [0, π/3]

Video transcript

Solve the following equation for X if X lies in the interval from zero to pi divided by five, where our equation is Y equals 1/6 code tangent of five X. And we have four possible answers being X equals 1/5 code tangent in verse Y divided by six, X equals five Kent and verse Y divided by six X equals 1/5 code tangent in verse six Y or X equals five co tangent inverse six Y. Now I will first write this equation and we want to try and solve for X with our equation. We have 1/6 cotangent five X to solve this. We first need to get rid of our fraction 1/6. We can do this by multiplying both sides by six, six Y equals code tangent five X. Next, we need to get rid of our code tangent because code tangent is our function that we need to move to the other side. We can change a code tangent by taking code tangent in verse of both sides. We get code tangent in verse six Y equals five X. Finally, we have five X, we can get rid of that by multiplying both sides by 1/5 that cancels out our five and one fits on the right side to give us X equals one fits cotangent inverse of six Y. We don't have any simplification to do so. Our answer corresponds with answer C OK. I hope that we solve the problem. Thank you for watching. Goodbye.