Trig Functions?

**nirva** · May 28th 2006, 10:51 PM

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.

**CaptainBlack** · May 29th 2006, 01:11 AM

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

**nirva** · May 29th 2006, 10:56 AM

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
$\int \frac {sin(x) + sec(x)} {tan(x)} dx$

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)?

**malaygoel** · May 29th 2006, 07:04 PM

yes it is equal to Csc(x)

**Soroban** · May 30th 2006, 04:16 AM

Hello, nirva!

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

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

What is $\frac{\sec x }{\tan x}$ equal to? . $\csc x$ ?

Yes . . . $\displaystyle{\frac{\sec x}{\tan x}\;=\;\frac{\frac{1}{\cos x}}{\frac{\sin x}{\cos x}} \;=\;\frac{1}{\cos x}\cdot\frac{\cos x}{\sin x} \;=\;\frac{1}\sin x} \;=\;\csc x }$

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

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

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

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

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

Then make two fractions:

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

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

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

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

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

. . . $\frac{12\cdot\left(\frac{1}{3} + \frac{1}{2}\right)}{12\cdot\left(\frac{1}{6} + \frac{1}{4}\right)} \;= \;\frac{4 + 6}{2 + 3} \;= \;\frac{10}{5}\;=\;2$ . . . see?

**Susie38** · May 30th 2006, 01:52 PM

Are you asking for the different trig identities? just wondering

Thread: Trig Functions?

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