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

Question

I have already got a response to this question that needs some clearing up. Assuming I don’t want to use the unit circle and just want to type this on my calculator, can someone explain the process (Rule that tangent repeats every 180 explanation would also be appreciated) Thank you for reading

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

Also answered here:

https://www.wyzant.com/resources/answers/696080/what-are-the-values-of-between-0-and-2pi-when-tan-1

Answer 2

Great!! If if you have a graphing calculator let say (ti-84), make sure to press MODE, arrow down until you see Radian, arrow to the right to change to DEGREE ( press enter) for the change to take place.

2) Press 2nd mode to go back to the clear window.

3) Now type 2nd tan or tan^-1 (-1) = and your answer will be -45º, or - π/4 but negative 45 degree is in the 4th quadrant , therefore the answer must be 315° or 7π / 4. but wait, this is not the only answer. That is why you have to think about the unit circle, the other quadrant where the tanθ=-1 is the second quadrant . In order to find that angle without the unit circle just add 180 to -45. 180-45 = 135 (second quadrant) or 3π/4.

4) I am sorry for the long explanation, Your answers are 7π/4 and 3π /4. or 315º and 135°. or (H)

Note: To check your answer(s): tan(315) =. -1 and tan(135)= -1.

tan(7Π/4) = -1 and tan(3Π/4) = -1