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

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Answer 1 · 2018-05-28T07:11:11

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

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'