How do you evaluate tan^-1(-1) without a calculator?

1 Answer
Dec 1, 2016

Depending upon if the domain is restricted to ((-pi)/2,pi/2) the solution will be pi/4 or if the domain is not restricted the solution will be pi/4+pik where k is an interger >=1

Explanation:

What you are trying to solve is

x=tan^-1(-1)

Since the problem deals with the inverse tangent, that means we will use the tangent function to solve the problem.

tan(x)=tan(tan^-1(1))

tan(x)=1

Now let's think about when tan(x)=1

If we are rotating an angle and dealing with a right triangle, we know that tan(45^@)=1/1=1 and tan(225^@)=(-1)/-1=1

Since you are more than likely discussing radians, x=pi/4, x=(5pi)/4, and we can continue to add pik where k is an integer>=1

Therefore x=pi/4+pik where k is an interger >=1.

If the domain is restricted to ((-pi)/2,pi/2) then the solution will be x=pi/4.