would the arctangent of -1 equal -π/4 or 7π/4?

Answer 1

There are in fact TWO (2) solutions

tan X = -1

sin X/ cos X = -1

sin X = -cos X

OR

-sin x = cos x

In the first quadrant, both sine and cosine are positive, so that's not it....

In the second quadrant, sine is positive while cosine is negative so a possible solution is in quadrant 2....

In the third quadrant, sine and cosine are both negative, so that's not it....

In the fourth quadrant, sine is negative and cosine is positive, so a possible solution is in quadrant 4...

In the first quadrant,

sin (pi/4) = sin(45 degrees) = sqrt(2)/2 = cos(pi/4) = cos(45 degrees)

So the solution is some "flavour" of 45 degrees, or pi/4

In quadrant 2, this is 180-45 = 135 = pi - pi/4 = 3*pi/4 is one solution

In quadrant 4, this is 360 - 45 = 315 = 2*pi - pi/4 = 7*pi/4 = -pi/4