For angles ranging from 0 to 360 degrees, tan(angle) gives the slope of a line passing through the origin.
Hence, we can represent it with 2 angles.
calculates the angle of a line with slope -1.
This is a line going through the origin at 45 degrees downward from left to right.
Hence, it's angle is 90+45=135 or -45 degrees.
You used radian mode on your calculator and you worked with the -45 degree angle.
It helps to understand that cos(angle) gives a horizontal co-ordinate in the unit-radius circle, centre (0,0).
Now, for this line, which co-ordinate will you find ?
Because, in the second quadrant, where the line cuts the circle,
the horizontal co-ordinate is negative.
For the angle you worked with (in the 4th quadrant), the horizontal co-ordinate is positive.
Hence there are 2 answers.
The one you quoted is correct, the other is the negative of that.
I'm not sure what you mean by "your teacher wants it in exact value". Is it surd form?
In that case, use the surd forms for