The measure of angle θ is 7π/4. the measure of its reference angle is __°, and tan θ is

Step-by-step explanation:

Even though I have been teaching calculus and precalc for several years now, my mind automatically wants to think in degrees as opposed to radians.  So I converted the angle from radians to degrees to get 315.  This angle lies in QIV.  The reference angle is a 45 degree angle, since 360 - 315 = 45.  This is a 45 degree angle, but if you consider direction, measuring clockwise gives you a negative angle.  So it could be that the reference angle needs to be identified as -45 degrees.  It depends upon what lesson you are dealing with.  Regardless, because this is a 45-45-90 right triangle, both the legs measure the same length (because of the Isosceles Triangle Theorem), which is 1.  Therefore, if the angle is 45 degrees, then the tangent of it is 1/1 = 1.