What are the values of θ, between 0 and 2pi, when tan θ=-1 ?

Question

Assuming I have no experience in trigonometry, how would I approach this problem? I know I can go about this by using the unit circle or special rights triangles but since I am inexperienced in trigonometry, an extremely detailed explanation would be very appreciated.

Answer Choices:

F: pi/4 and 3pi/4 only

G: 3pi/4 and 5pi/4 only

H: 3pi/4 and 7pi/4 only

J: 5pi/4 and 7pi/4 only

K: pi/4, 3pi/4, 5pi/4, and 7pi/4 only

Answer 1

Based on your situation, assuming you do NOT wish to relearn the unit circle (which I believe is a mistake, BTW), perhaps the best way is to just use your calculator and the rule that tangent (and cotangent) repeat every 180°.

To use your calculator, to find the angle where the tangent is a given number, you would use the tan^-1 button (usually its the "2nd function" "tan" button). In this case, type into your calculator tan^-1(-1) and you will probably get -45° (that's what my TI-84 Plus CE says anyway). Now you have to realize that -45° is the same as 315° and they are both the same as 7pi/4 (separate discussion). Now, use the rule that tangent repeats every 180° (or pi radians) to back off from 7pi/4 by pi radians (aka 4pi/4) to get 3pi/4 (7pi/4 - 4pi/4 = 3pi/4). So the answer is H.