Question

please put answers for sin, cos, tan, cot, sec, and csc

Answer 1

If we measure the angle in the clockwise direction:

Therefore, this point is:

$(-1,0)$

Since the cosine and sine functions are given by:

$\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \end{gathered}$

Therefore:

$\begin{gathered} \sin (-\pi)=\frac{0}{1}=0 \\ \cos (-\pi)=\frac{1}{-1}=-1 \end{gathered}$

Since:

$\begin{gathered} \cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}\to\cot (-\pi)=-\frac{1}{0}=_{\text{ }}undefined \\ \csc (\theta)=\frac{hypotenuse}{_{\text{ }}opposite}\to\csc (-\pi)=\frac{1}{0}=_{\text{ }}undefined \end{gathered}$

Therefore, we can conclude that cotangent and cosecant are undefined for - π

$\begin{gathered} \tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}=\frac{0}{-1}=0 \\ \sec (\theta)=\frac{hypotenuse}{_{\text{ }}adjacent}=\frac{1}{-1}=-1 \end{gathered}$