Respuesta :
Answer:
The exact values of trignometric functions [tex]cos\theta, csc\theta and tan\theta[/tex] are [tex]cos\theta=-\frac{3}{\sqrt{13}}[/tex] , [tex]csc\theta=-\frac{\sqrt{13}}{2}[/tex] and [tex]tan\theta=\frac{2}{3}[/tex]
Step-by-step explanation :
To find the exact values of trignometric functions [tex]cos\theta, csc\theta and tan\theta[/tex]
First we have to find r:
[tex]r^2=x^2+y^2[/tex]
Let (x,y) be the given point (-3,-2)
[tex]r=\sqrt{x^2+y^2}[/tex]
Now substitute the x and y values in above equation
[tex]r=\sqrt{(-3)^2+(-2)^2}[/tex]
[tex]=\sqrt{9+4}[/tex]
[tex]=\sqrt{13}[/tex]
Therefore [tex]r=\sqrt{13}[/tex]
Now to find these trignometric values of [tex]cos\theta, csc\theta and tan\theta[/tex]
[tex]cos\theta=\frac{x}{r}[/tex]
[tex]=\frac{-3}{\sqrt{13}}[/tex]
Therefore [tex]cos\theta=-\frac{3}{\sqrt{13}}[/tex]
[tex]csc\theta=\frac{r}{y}[/tex]
[tex]=\frac{\sqrt{13}}{-2}[/tex]
Therefore [tex]csc\theta=-\frac{\sqrt{13}}{2}[/tex]
[tex]tan\theta=\frac{y}{x}[/tex]
[tex]=\frac{-2}{-3}[/tex]
Therefore [tex]tan\theta=\frac{2}{3}[/tex]
Therefore the exact values of trignometric functions [tex]cos\theta, csc\theta and tan\theta[/tex] are [tex]cos\theta=-\frac{3}{\sqrt{13}}[/tex] , [tex]csc\theta=-\frac{\sqrt{13}}{2}[/tex] and [tex]tan\theta=\frac{2}{3}[/tex].
