Question

Find each value by referring to the graphs of the trigonometric functions?

Answer 1

check the picture below.

notice, go around a full circle "clockwise", or backwards, we'd get the negative angles, a full circle will be -2π, go around again, and is -2π-2π or -4π.

now, notice the last bit, the red angle, we went around -π more after the -4π, which makes it -5π.

therefore, the cot(-5π) is the same value as the cot(π),


`\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\qquad \qquad cot(-5\pi )\implies cot(\pi )=\cfrac{cos(\pi )}{sin(\pi )} \\\\\\ cot(\pi )=\cfrac{-1}{0}\impliedby und efined`


meaning it doesn't have one.