Which of the following angles are coterminal to θ=5π/6?
Select all that are True.
30∘
−11π/6
−7π/6
−330∘
17π/6
I think itś -11.5/6
thank you
5π/6 = 150°
5π/6 + 2π = 17π/6 = 510°
5π/6 - 2π = -7π/6 = -210°
To find the coterminal angles of θ=5π/6, we need to add or subtract multiples of 2π until we get equivalent angles.
The given angles are:
30∘
−11π/6
−7π/6
−330∘
17π/6
To convert 5π/6 to degrees, we can multiply by 180/π:
(5π/6) * (180/π) = 150 degrees
Now, let's check which angles are coterminal with 5π/6:
30∘: This angle is not coterminal with 5π/6 because it is not equal to 150 degrees.
−11π/6: This angle is coterminal with 5π/6 because when we add 2π, we get:
−11π/6 + 2π = −11π/6 + 12π/6 = π/6
π/6 is also the same as 30 degrees, so −11π/6 is coterminal with 5π/6.
−7π/6: This angle is not coterminal with 5π/6 because it is not equal to 150 degrees.
−330∘: This angle is coterminal with 5π/6 because when we add 360 degrees, we get:
−330∘ + 360∘ = 30∘
30 degrees is the same as 5π/6, so −330∘ is coterminal with 5π/6.
17π/6: This angle is not coterminal with 5π/6 because it is not equal to 150 degrees.
So, the coterminal angles to θ=5π/6 are:
−11π/6
−330∘
To find the coterminal angles to θ=5π/6, you need to add or subtract any multiple of 2π to θ.
Given θ=5π/6, to find the coterminal angles, you can add or subtract a full revolution, which is 2π radians, to find other angles that are equivalent.
To add a full revolution, you can add 2π to θ:
θ + 2π = 5π/6 + 2π = 5π/6 + 12π/6 = 17π/6
Therefore, 17π/6 is coterminal to θ=5π/6.
To subtract a full revolution, you can subtract 2π from θ. To make calculations easier, you can express 2π as 12π/6 because 2π is equivalent to 12π/6.
θ - 12π/6 = 5π/6 - 12π/6 = -7π/6
Therefore, -7π/6 is coterminal to θ=5π/6.
So, the coterminal angles to θ=5π/6 are:
-7π/6 and 17π/6.
Now let's check which options are coterminal angles to θ=5π/6:
30∘: To compare this angle with θ=5π/6, we need to convert it to radians. 30∘ is equal to π/6 radians. Since π/6 radians is not equal to 5π/6, 30∘ is not coterminal to θ=5π/6.
-11π/6: We have already found that -7π/6 is coterminal to θ=5π/6. -11π/6 is equivalent to -7π/6 when expressed in a positive form. Therefore, -11π/6 is coterminal to θ=5π/6.
-7π/6: This is one of the coterminal angles we found earlier. Therefore, -7π/6 is coterminal to θ=5π/6.
-330∘: To compare this angle with θ=5π/6, we need to convert it to radians. -330∘ is equivalent to -11π/6 radians. We have already found that -7π/6 is coterminal to θ=5π/6. Therefore, -330∘ is also coterminal to θ=5π/6.
17π/6: This is the other coterminal angle we found earlier. Therefore, 17π/6 is coterminal to θ=5π/6.
Among the given options, the angles that are coterminal to θ=5π/6 are:
-11π/6
-7π/6
-330∘
17π/6
Therefore, your choice of -11.5/6 is correct.