Answer:
[tex]\cot(-\theta)=-\cot(\theta)[/tex]
and
[tex]\cot(\theta+\pi)=\cot(\theta)[/tex]
Step-by-step explanation:
Justin wants to evaluate
[tex]3\cot(-\frac{5\pi}{4})[/tex].
First he can use the fact that, the cotangent function is an odd function and write.
[tex]3\cot(\frac{5\pi}{4})=-3\cot(\frac{5\pi}{4})[/tex].
Also the cotangent function is positive in both the first and third quadrant, so we can use the symmetric property;
[tex]-3\cot(\pi+\frac{\pi}{4})=-3\cot(\frac{\pi}{4})[/tex].
Hence the correct answers are;
[tex]\cot(-\theta)=-\cot(\theta)[/tex]
and
[tex]\cot(\theta+\pi)=\cot(\theta)[/tex]
