IDENTIFY THE ANGLE THAT IS NOT COTERMINAL WITH OTHERS

Example 1 :

Identify the angle measure that is not coteminal with other angle measures.

-120°, 600°, -480°, 180°, 240°

Solution :

Step 1 :

Find the angles that are least and largest among the given angle measures.

Least angle  =  -480°

Largest angle  =  600°

Step 2 :

Add 360° to -480°. Again add 360° to the result and so on.

Continue this process until you get 600° or larger than 600°.

-480° + 360°  =  -120°

-120° + 360°  =  240°

240° + 360°  =  600°

Step 3 :

In step 2, the resulting angle measures are

-120°, 240°, 600°

Comparing the resulting angles measures and the given angle measures, 180° in the given angle measures is not found in the list of resulting angle measures.

So, in the given angle measures, 180° is not coterminal with others.

Example 2 :

Identify the angle measure that is not coteminal with other angle measures.

π/5, 49π/5, 21π/5, -9π/5, 11π/5

Solution :

Step 1 :

Find the angles that are least and largest among the given angle measures.

Least angle  =  -9π/5

Largest angle  =  49π/5

Step 2 :

Add 2π to -9π/5. Again add 2π to the result and so on.

Continue this process until you get 49π/5 or larger than 49π/5.

. 

-9π/5 + 2π  =  -9π/5 + 10π/5  =  π/5

π/5 + 2π  =  π/5 + 10π/5  =  11π/5

11π/5 + 2π  =  11π/5 + 10π/5  =  21π/5

21π/5 + 2π  =  21π/5 + 10π/5  =  31π/5

31π/5 + 2π  =  31π/5 + 10π/5  =  41π/5

41π/5 + 2π  =  41π/5 + 10π/5  =  51π/5 > 49π/5

Step 3 :

In step 2, the resulting angle measures are

π/5, 11π/5, 21π/5, 31π/5, 41π/5, 51π/5

Comparing the resulting angles measures and the given angle measures, 49π/5 in the given angle measures is not found in the list of resulting angle measures.

So, in the given angle measures, 49π/5 is not coterminal with others.

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