Question

The terminal side of `theta` in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of `theta`?

Answer 1

See explanation.

Explanation:

If you have a point ion the terminal side `(x,y)` then you have to calculate the didtance between the point and the origin

`r=sqrt(x^2+y^2)`

`r=sqrt(0^2+3^2)=3`

Now the trig functions are defined as:

`sin theta=y/r`

`sin theta=0/3=0`

`cos theta=x/r`

`cos theta=3/3=1`

`tan theta=y/x`

`tan theta=0/3`

`cot theta=x/y`

`cot theta=3/0` `cot theta` is undefined.

`sec theta=r/x`

`sec theta=3/3=1`

`csc theta=r/y`

`csc theta=3/0` `csc theta` is undefined