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)=(0)/(1)=0 \\ \cos (-\pi)=(1)/(-1)=-1 \end{gathered}`

Since:

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

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