DETERMINE IF TWO ANGLES ARE COTERMINAL

Example 1 :

Determine the following pairs of angles are coterminal.

380°, 20°

Solution :

Step 1 :

Find the difference between the given two angle measures.

380° - 20° = 360°

Step 2 :

The result of step 1 is

= 360°

= 1(360°)

which is a multiple of 360°.

So, 380° and 20° are coterminal angles.

Example 2 :

Determine the following pairs of angles are coterminal.

40°, 400°

Solution :

Step 1 :

Find the difference between the given two angle measures.

40° - 400° = -360°

Step 2 :

The result of step 1 is

= -360°

= -1(360°)

which is a multiple of 360°.

So, 40° and 400° are coterminal angles.

Example 3 :

Determine the following pairs of angles are coterminal.

200°, -520°

Solution :

Step 1 :

Find the difference between the given two angle measures.

200° - (-520°) = 200° + 520°

200° - (-520°) = 720°

Step 2 :

The result of step 1 is

= 720°

= 2(360°)

which is a multiple of 360°.

So, 200° and -520° are coterminal angles.

Example 4 :

Determine the following pairs of angles are coterminal.

-60°, -600°

Solution :

Step 1 :

Find the difference between the given two angle measures.

-60° - (-600°) = -60° + 600°

-60° - (-600°) = 540°

Step 2 :

The result of step 1 is

= 540°

which is not a multiple of 360°.

So, -60° and -6000° are not coterminal angles.

Example 5 :

Determine the following pairs of angles are coterminal.

π/9, -35π/9

Solution :

Step 1 :

Find the difference between the given two angle measures.

π/9 - (-35π/9) = π/9 + 35π/9

π/9 - (-35π/9) = (π + 35π) / 9

π/9 - (-35π/9) = 36π/9

π/9 - (-35π/9) = 36π/9

π/9 - (-35π/9) = 4π

Step 2 :

The result of step 1 is

= 4π

= 2(2π)

which is a multiple of 2π.

So, π/9 and -35π/9 are coterminal angles.

Example 6 :

Determine the following pairs of angles are coterminal.

5π/6, 5π/2

Solution :

Step 1 :

Find the difference between the given two angle measures.

5π/6 - 5π/2 = 5π/6 - 15π/6

5π/6 - 5π/2 = (5π - 15π) / 6

5π/6 - 5π/2 = -10π/6

5π/6 - 5π/2 = -5π/3

Step 2 :

The result of step 1 is

= -5π/3

which is not a multiple of 2π.

So, 5π/6 and 5π/2 are not coterminal angles.

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