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

Mar 22, 2018

$\text{cosec } \theta = \frac{h}{o} = \frac{5}{3}$

$\text{sec } \theta = \frac{h}{a} = \frac{5}{4}$

$\text{tan } \theta = \frac{a}{o} = \frac{4}{3}$

#### Explanation:

If you have a point $P$ at $\left(3 , 4\right)$ 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.

$\text{cosec } \theta = \frac{h}{o} = \frac{5}{3}$

$\text{sec } \theta = \frac{h}{a} = \frac{5}{4}$

$\text{tan } \theta = \frac{a}{o} = \frac{4}{3}$