Stephanie M. answered • 05/15/15

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Co-terminal angles are separated by multiples of 2π radians. So, let's add or subtract 2π = (16π)/8 from each possible answer choice to see which ones are coterminal with (5π)/8:

(a)

(-13π)/8 + (16π)/8 = (3π)/8

(3π)/8 + (16π)/8 = (19π)/8

We've gone past (5π)/8 without hitting it, so this angle

**is****not****co-terminal**.(b)

(21π)/8 - (16π)/8 = (5π)/8

This angle is a multiple of 2π away from (5π)/8, so it

**is co-terminal**.(c)

(37π)/8 - (16π)/8 = (21π)/8

(21π)/8 - (16π)/8 = (5π)/8

This angle is a multiple of 2π away from (5π)/8, so it

**is co-terminal**.(d)

(-11π)/8 + (16π)/8 = (5π)/8

This angle is a multiple of 2π away from (5π)/8, so it

**is co-terminal**.