Question

The terminal side of `theta` in standard position contains (4,-2), how do you find the exact values of the six trigonometric functions of `theta`?

Answer 1

See explanation.

Explanation:

The point's coordinates are:

`x=4`, `y=-2`

To calculate the functions we have to calculate the distance between the point and the origin:

`r=sqrt(x^2+y^2)=sqrt(4^2+(-2)^2)=sqrt(16+4)=sqrt(20)=2sqrt(5)`

Now we can calculate the functions:

`sintheta=y/r=-2/(2sqrt(5))=-sqrt(5)/5`

`costheta=x/r=4/(2sqrt(5))=2/sqrt(5)=(2sqrt(5))/5`

`tantheta=y/x=-2/4=-1/2`

`cottheta=x/y=4/-2=-2`

`sectheta=r/x=(2sqrt(5))/4=sqrt(5)/2`

`csctheta=r/y=(2sqrt(5))/-2=-sqrt(5)`