Question

What is the csc, sec, and cot of point (3,4)?

Answer 1

`"cosec " theta = h/o = 5/3`

`"sec " theta = h/a = 5/4`

`"tan " theta = a/o = 4/3`

Explanation:

If you have a point `P` at `(3,4)` you can draw a triangle from the origin.

A point cannot have a trig ratio, only an angle can. Assuming you mean the angle formed at `P`. Call it `theta`

The lengths of the sides will be as follows:

The horizontal line on the `x`-axis will be `3` units long.
This is the side opposite `theta`.

The vertical line along the line `x=3` will be `4` units long.
This is the side adjacent to `theta`

By Pythagoras, the hypotenuse from the origin to `P` will be `5` units.

NOw that we have the sides defined and we know their lengths we can determine the ratios.

`"cosec " theta = h/o = 5/3`

`"sec " theta = h/a = 5/4`

`"tan " theta = a/o = 4/3`