Determine which of the following does NOT represent an angle co terminal...

Question

Determine which of the following does NOT represent an angle co terminal with the given angle θ= 5π/8?

 

a) -13π/8

 

b) 21π/8

 

c) 37π/8

 

d) -11π/8

 

 

Answer 1

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.