What is the SMALLEST POSITIVE ANGLE that is coterminal with the angle having the radian measure of -10π/3?

Is there any solution for this kind of question?

just keep adding 2π till you get a positive value.

2π = 6π/3, so you get

-10π/3 + 6π/3 = -4π/3 + 6π/3 = 2π/3
and we have a winner!

Yes, there is a solution for this kind of question. To find the smallest positive angle that is coterminal with a given angle, you can use the concept of coterminal angles. Coterminal angles are angles that have the same initial side and terminal side (i.e., they point in the same direction).

To find the smallest positive angle that is coterminal with the angle -10π/3, we can add or subtract any multiple of 2π (360 degrees) to the given angle until we get a positive angle.

In this case, we have -10π/3. To make it positive, we can add 2π repeatedly until we get a positive angle:

-10π/3 + 2π = -10π/3 + 6π/3 = -4π/3

Now, -4π/3 is still negative, so we add another 2π:

-4π/3 + 2π = -4π/3 + 6π/3 = 2π/3

2π/3 is still negative, so we add another 2π:

2π/3 + 2π = 2π/3 + 6π/3 = 8π/3

Finally, 8π/3 is positive, and it is the smallest positive angle that is coterminal with -10π/3.

Therefore, the answer is 8π/3.

Yes, there is a solution for this kind of question. To find the smallest positive angle that is coterminal with -10π/3 radians, we can use the following steps:

1. Convert the given angle from radians to degrees. To do this, we can use the formula: degrees = radians * (180/π).
So, -10π/3 * (180/π) = -600/3 = -200 degrees.

2. Add 360 degrees to the converted angle to find a coterminal angle. Since we want the smallest positive angle, we need to add multiples of 360 until we get a positive value.
-200 + 360 = 160 degrees.

Therefore, the smallest positive angle that is coterminal with -10π/3 radians is 160 degrees.