Why does the calculator answer of -45° instead of 135° when I put in -1 and press the tan^-1 button

Why does the calculator answer of -45° instead of 135° when I put in -1 and press the tan^-1 button?

There are infinitely many solutions to the equation tan(x) = -1.
Your calculator probably chooses the one that is between -90° and +90°. That's in accordance with the general convention: http://en.wikipedia.org/wiki/Arctan Some calculators might choose the one that is between 0° and 180° and it sounds as if you would prefer that. If your calculator gives you a negative answer for such an inverse tan calculation and you would prefer a positive one, simply add 180° (the tan function repeats every 180°).

This has to do with cotermimal angles.

0 is coterminal to 2pi is coterminal with 4pi, etc.

There.are an infinite number of angles that will have a frog function value.associated.with them.
Them it is important to realize what range calculators take troy angles to and how to manipulate those angles.to get the angle you want.

Sin and tan go to -pi/2 to pi/2 (-90 to 90)
Cos goes.from 0 to pi. (0-180)

Remember, points on the unit circle can be written as (cost, sint) too. This will help you see identities like cost=cos(180-t) and others.

hope this helps.some.

-45 is the same as 135 in terms of tan, since as the other person who answered has said, there is basically an infinite amount of solutions, going up in incriments of 180 degrees.

e.g. tan20=tan200
tan200=tan380
etc...

Is your calculator in radians? It should be in degree mode for sine, cosine, tangents and their inverses.