# Trig Functions?

• May 28th 2006, 10:51 PM
nirva
Trig Functions?
I'm wondering if someone could help me list the Trig functions series.
For example:

Tan(x) = Sin(x)/Cos(x)
Sec(x) = 1/Cos(x)

I'm not sure if this is posted in the right section but I need these information for my Calc homeworks.
• May 29th 2006, 01:11 AM
CaptainBlack
Quote:

Originally Posted by nirva
I'm wondering if someone could help me list the Trig functions series.
For example:

Tan(x) = Sin(x)/Cos(x)
Sec(x) = 1/Cos(x)

I'm not sure if this is posted in the right section but I need these information for my Calc homeworks.

Are you sure that the examples give are what is expected?

Others are:

Cot(x)=1/Tan(x)=Cos(x)/Sin(x)
Cosec(x)=1/Sin(x).

RonL
• May 29th 2006, 10:56 AM
nirva
Quote:

Originally Posted by CaptainBlack
Are you sure that the examples give are what is expected?

Others are:

Cot(x)=1/Tan(x)=Cos(x)/Sin(x)
Cosec(x)=1/Sin(x).

RonL

Because those examples are what was given to some question like
$\displaystyle \int \frac {sin(x) + sec(x)} {tan(x)} dx$

Where sin(x)/tan(x) becomes sin(x)/{sin(x)/cos(x)}
What is Sec(x)/Tan(x) equal to by the way? Csc(x)?
• May 29th 2006, 07:04 PM
malaygoel
yes it is equal to Csc(x)
• May 30th 2006, 04:16 AM
Soroban
Hello, nirva!

Quote:

Because those examples are what was given to some question like: $\displaystyle \int\frac{\sin x + \sec x}{\tan x}\,dx$

Where $\displaystyle \frac{\sin x}{\tan x }$ becomes $\displaystyle \frac{\sin x}{\frac{\sin x}{\cos x}}$

What is $\displaystyle \frac{\sec x }{\tan x}$ equal to? .$\displaystyle \csc x$ ?
Yes . . . $\displaystyle \displaystyle{\frac{\sec x}{\tan x}\;=\;\frac{\frac{1}{\cos x}}{\frac{\sin x}{\cos x}} \;=\;\frac{1}{\cos x}\cdot\frac{\cos x}{\sin x} \;=\;\frac{1}\sin x} \;=\;\csc x }$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

By the way, I prefer to simplify the function like this:

. . . $\displaystyle \displaystyle{\frac{\sin x + \sec x}{\tan x} \;= \;\frac{\sin x + \frac{1}{\cos x}}{\frac{\sin x}{\cos x}} }$

Multiply top and bottom by $\displaystyle \cos x$ **

. . . $\displaystyle \frac{\cos x\left(\sin x + \frac{1}{\cos x}\right)}{\cos x\left(\frac{\sin x}{\cos x}\right)} \;= \;\frac{\sin x\cos x + 1}{\sin x}$

Then make two fractions:

. . . $\displaystyle \frac{\sin x\cos x}{\sin x} + \frac{1}{\sin x} \;= \;\cos x + \csc x$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**
This is a technique used on a complex fraction,
. . a fraction with more than two "levels".

Example: $\displaystyle \frac{\frac{1}{3} + \frac{1}{2}}{\frac{1}{6} + \frac{1}{4}}$

Multiply top and bottom by the LCD of $\displaystyle all$ the denominators (12):

. . . $\displaystyle \frac{12\cdot\left(\frac{1}{3} + \frac{1}{2}\right)}{12\cdot\left(\frac{1}{6} + \frac{1}{4}\right)} \;= \;\frac{4 + 6}{2 + 3} \;= \;\frac{10}{5}\;=\;2$ . . . see?
• May 30th 2006, 01:52 PM
Susie38
Are you asking for the different trig identities? just wondering