Question

The question is in the image. Answer the question 4.

Answer 1

Step 1

Given;

`coordinate\text{ points\lparen5,-12\rparen}`

Required; To find the value of θ

Step 2

We use the trigonometric function Toa to find the required angle.

`\begin{gathered} tan\theta=(opposite)/(Adjacent) \\ opposite=-12 \\ adjacent=5 \\ tan\theta=(-12)/(5) \\ \end{gathered}`
`\begin{gathered} Using\text{ pythagoras} \\ (-12)^2+(5)^2=hypotenuse^2 \\ hypotenuse=√(144+25)=13 \\ Sin\theta=(opposite)/(Hypotenuse)=(-12)/(13) \end{gathered}`
`\begin{gathered} cos\theta=(adjacent)/(hypotenuse)=(5)/(13) \\ csc\theta=(1)/(sin\theta)=(1)/((-12)/(13))=(13)/(-12) \end{gathered}`
`\begin{gathered} sec\theta=(1)/(cos\theta)=(1)/((5)/(13))=(13)/(5) \\ cot\theta=(1)/(tan\theta)=(1)/((-12)/(5))=(5)/(-12) \end{gathered}`