Question

(-9,-4)Trig: the point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle.Sin(0) =Cos(0)=Tan(0)=Csc(0)=Sec(0)=

Answer 1

Given the point (-9,-4) that is on on the terminal side of an angle in standard position.

`x=-9,y=-4`

First, we determine the value of r, the hypotenuse.

`\begin{gathered} r^2=(-9)^2+(-4)^2 \\ r^2=81+16 \\ r^2=97 \\ r=√(97) \end{gathered}`

(a) Sin (θ)

`\begin{gathered} \sin \theta=\frac{Opposite}{\text{Hypotenuse}} \\ =(y)/(r) \\ =(-4)/(√(97)) \\ =-(4√(97))/(97) \end{gathered}`

(b) Cos (θ)

`\begin{gathered} \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}} \\ =(x)/(r) \\ =(-9)/(√(97)) \\ =-(9√(97))/(97) \end{gathered}`

(c) Tan (θ)

`\begin{gathered} \tan \theta=\frac{\text{Opposite}}{\text{Adjacent}} \\ =(y)/(x) \\ =(-4)/(-9) \\ =(4)/(9) \end{gathered}`

(d) csc (θ)

`\begin{gathered} \cosec \theta=(1)/(\sin \theta) \\ =-(√(97))/(4) \end{gathered}`

(e)sec(θ)

`\begin{gathered} \sec \theta=(1)/(\cos \theta) \\ =-(√(97))/(9) \end{gathered}`