# Thread: Sec, cot, csc

1. ## Sec, cot, csc

What does sec, cot and csc stand for in Trig. When you are trying to find something in degrees and pi wise. Like

sec (30 degrees) * cot (45 degress

sec pi - csc (pi/2)

Is there a certain number that sec, cot, and csc stand for like sin, cos, and tan?

2. You should have definitions:

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = 1/tan(x)

3. Originally Posted by christenc05
What does sec, cot and csc stand for in Trig. When you are trying to find something in degrees and pi wise. Like

sec (30 degrees) * cot (45 degress

sec pi - csc (pi/2)

Is there a certain number that sec, cot, and csc stand for like sin, cos, and tan?
What are they:
They are reciprocal for $\sin x$, $\cos x$, $\tan x$.

$\mathrm{sec}x = \frac{1}{\cos x}$, $\mathrm{csc}x=\frac{1}{\sin x}$, $\mathrm{cot}x = \frac{1}{\tan x}$.

Calculation:
You can change it in terms of $\sin x$, $\cos x$, $\tan x$ and work with them.

Question 1:
$\sec(30^\circ) * \cot(45^\circ)$
$= \frac{1}{\cos(30^\circ)} * \frac{1}{\tan(45^\circ)}$
$=\frac{1}{\frac{\sqrt{3}}{2}} * \frac{1}{1}$
$=\frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$

Question 2:
$\sec\left(\pi\right) - \csc \left(\frac{\pi}{2}\right)$
$\frac{1}{\cos \left(\pi\right)} - \frac{1}{\sin \left(\frac{\pi}{2}\right)}$
$=\frac{1}{-1} - \frac{1}{1}$
$=-2$

4. Originally Posted by Air
What are they:
They are ${\color{red}inverse}$ for $\sin x$, $\cos x$, $\tan x$.
Careful here, would you like to restate that maybe?

5. Originally Posted by Mathstud28
Careful here, would you like to restate that maybe?
Hmm...Help me with the wording. I mean that it's 1 over the function.

EDIT: Got it, it's the reciprocal.

6. Originally Posted by Air
Hmm...Help me with the wording. I mean that it's 1 over the function.
They are not inverse functions, they are reciprocals of the normal trigonometric functions.

Inverse would be like $\arccos(x),\arctan(x)$ etc.

Thanks for helping though, great working just a little off on the terminology.

7. Originally Posted by Mathstud28
They are not inverse functions, they are reciprocals of the normal trigonometric functions.

Inverse would be like $\arccos(x),\arctan(x)$ etc.

Thanks for helping though, great working just a little off on the terminology.
Lol ! That's funny, in France it's exactly the inverse opposit
Litterally, inverse would be 1/... and reciprocal would be arctan, etc...
Pretty confusing !

8. Originally Posted by Moo
Lol ! That's funny, in France it's exactly the inverse opposit
Litterally, inverse would be 1/... and reciprocal would be arctan, etc...
Pretty confusing !
Yeah, haha, here the same can be said of numbers

The inverse and reciporcal of some number a are both interpreted as $\frac{1}{a}$

Where as in functions the definiton would probably be given by

Let $f(x)$ be a function, then $g(x)$ is a reciprocal function iff $f(x)\cdot{g(x)}=1$

and $g(x)$ is an inverse function iff

$f(g(x))=x$

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