Find the angle between 0 and 2𝜋 that is equivalent to 67/4𝜋.

Answer 1

64pi/4 + 3pi/4 = 67pi/4

64pi/4 = 16pi = 8*(2pi) = 8*0 = 0, therefore you are left with 3pi/4.

Answer 2

Angles of the form θ and (θ + n*2π) where n is an integer are equivalent, so we need to express (67/4)π as

(67/4)π = θ + n*2π

for an integer n, then θ will be the angle between 0 and 2π

To do this, we express (67/4)π as a mixed fraction

(67/4)π = (3/4)π + 16π

This can be rewritten to match the equation above

(67/4)π = (3/4)π + 8*2π

So the unique angle between 0 and 2π is (3/4)π