Solve the equation on the interval 0 <= theta < 2pi for cot (theta) = 2. I know the answer is .46,3.61, but I don't know how to arrive at that answer on a ti-84 calculator.

If cot(theta_ = 2, tan(theta) = 1/2

tan^-1(0.5) is 0.464 radians (26.57 degrees)

I don't have a TI-84 but your calculator should have a tan^-1 (arctan) function key. Make sure you are in the radians mode for angles.

The other angle with arctan 1/2 in that 0 to 2pi interval is in the third quadrant and is pi + 0.464 = 3.606 radians

To solve the equation cot(theta) = 2 on a TI-84 calculator, you can follow these steps:

1. Press the "MODE" button on your calculator. Make sure that the mode is set to "RADIAN" instead of "DEGREE". This is important because we want to solve the equation on the interval 0 <= theta < 2pi in radians.

2. Press the "2ND" button followed by the "TAN" button to access the cotangent function (cot). Enter "2" after the cot function to form cot^(-1)(2).

3. Press "ENTER" to calculate the inverse cotangent of 2. The calculator will display the principal value of cot^(-1)(2) in radians. Let's call this value "x".

4. To find the other solutions on the interval 0 <= theta < 2pi, you need to add or subtract multiples of pi.

a. To find the first solution, use the value of "x" as it is.
b. To find the second solution, add pi to "x".
c. To find the third solution, subtract pi from "x".

5. Once you have the three solutions, convert them to decimal form.

Note: Remember that the decimal form of angles is often rounded to a certain number of decimal places. In this case, you mentioned that the answer is 0.46 and 3.61.

By following these steps, you can solve the equation cot(theta) = 2 on a TI-84 calculator and obtain the solutions you provided: 0.46 and 3.61.