Step 1
Given;
[tex]coordinate\text{ points\lparen5,-12\rparen}[/tex]
Required; To find the value of θ
Step 2
We use the trigonometric function Toa to find the required angle.
[tex]\begin{gathered} tan\theta=\frac{opposite}{Adjacent} \\ opposite=-12 \\ adjacent=5 \\ tan\theta=\frac{-12}{5} \\ \end{gathered}[/tex][tex]\begin{gathered} Using\text{ pythagoras} \\ (-12)^2+(5)^2=hypotenuse^2 \\ hypotenuse=\sqrt{144+25}=13 \\ Sin\theta=\frac{opposite}{Hypotenuse}=\frac{-12}{13} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse}=\frac{5}{13} \\ csc\theta=\frac{1}{sin\theta}=\frac{1}{\frac{-12}{13}}=\frac{13}{-12} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{5}{13}}=\frac{13}{5} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{-12}{5}}=\frac{5}{-12} \end{gathered}[/tex]
