Given t ≈ 9.4 is a solution to cot t = –40.35, use the period of the function to name three additional solutions.

Given t ≈ 9.4 is a solution to cot t = –40.35, use the period of the function to name three additional solutions.

 

tan is negative in  the second and forth quadrants. 

Since cot is the reciprocal of tan, it is negative in the second and 4th quadrants too.

So the solutions for t will be at pi radian intervals

 

t cannot be measured in degrees because cot of 9.4 degrees would be positive so t must be measured in radians.

 

So the general solution for t must be 

\(t=9.4-n\pi \qquad n\in z\)In other words n is in the set of integers

so here are 3 more solutions

 

\(t=9.4-\pi\\ t=9.4-2\pi\\ t=9.4-\pi\\\)