Question

How do you find all six trigonometric functions of θ if the given point (5,0) is on the terminal side of θ?

Answer 1

Use the side lengths as `1,0,1` to define the ratios.

Explanation:

This is one of the special triangles.

The fact that the point is on the `x-`axis means that the angle at `(0,0)` is actually `0°` and the side opposite it has a length of `0`.

The sides are as follows:

Adjacent = `5`
opposite = `0`
Hypotenuse = `5`

Using these values you can define the 6 ratios of `0°`

`sin 0° = o/h = 0/5=0`

`cos 0° = a/h = 5/5= 1`

`tan 0° = o/a = 0/5=0`

`cot 0° = a/o = 5/0 = oo` or undefined

`sec 0° = h/a = 5/5=1`

`sin 0°= h/o = 5/0 = oo` or undefined.

You can also determine the ratios of `90°` using this 'triangle'