What is the measure of an angle θ that is coterminal with an angle of measure −17π6 where 0≤θ≤2π.

Answer 1

-17pi/6 is coterninal with 4pi-17pi/6 = (24pi-17pi)/6 = 7pi/6 radians = 240 degrees

Answer 2

Hello Hamza,

To find coterminal angles, you either add OR subtract 2π as many times as needed.

Here, you are starting from -17π/6 and want to find a coterminal angle between 0 and 2π. In this case, subtracting 2π from -17π/6 will only make your answers more negative and further away from [0, 2π] so you will want to ADD instead.

-17π/6 + 2π = -17π/6 + 12π/6 = -5π/6 This answer doesn't fall in the [0,2π] interval so we gotta add 2π at least one more time

-5π/6 + 2π = -5π/6 + 12π/6 = 7π/6 Bingo. There we got a coterminal angle that's between 0 and 2π.

So: final answer is 7π/6