Question

How can we find tan inverse of a number without calculator,for eg. Tan inverse of -1 ?

Answer 1

`tan^(-1)x` can be found without a calculator only for some special values of `x`.

Explanation:

For example, `tan^(-1)(-1)=-pi/4`. This is because `sin(-pi/4)=-sqrt2/2` and `cos(-pi/4)=sqrt2/2`, so `tan(-pi/4)=-1`.

In general, `tan^(-1)(x)=theta` implies that `tan(theta)=x`, remembering that `theta` can only take on values from `-pi/2` to `pi/2`. Therefore, to find `tan^(-1)x` you need to think about what value of `theta` would satisfy `tan(theta)=x`?