The only quadrant where `sec theta` is positive and `sin theta` is negative is Quadrant IV.

Considering the reference angle `alpha` in the first quadrant, we let `sec α = 1.122`, giving `cos alpha=1/1.122=0.8912656`.

So `alpha = arccos 0.8912656 = 27.0^@`

We now use that reference angle to find the value of `theta` in the fourth quadrant.

So ` θ = 360^@ − 27.0^@ = 333.0^@`

Finally, we find the `cot` of that fourth quadrant angle.

So `cot theta=1/(tan 333.0^@)=-1.963`