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

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Answer 1 · 2018-03-22T20:33:22

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

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

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

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.

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

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

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