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.
Because those examples are what was given to some question likeOriginally Posted by CaptainBlack
$\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)?
Hello, nirva!
Yes . . . $\displaystyle \displaystyle{\frac{\sec x}{\tan x}\;=\;\frac{\frac{1}{\cos x}}{\frac{\sin x}{\cos x}} \;=\;\frac{1}{\cos x}\cdot\frac{\cos x}{\sin x} \;=\;\frac{1}\sin x} \;=\;\csc x }$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? .$\displaystyle \csc x$ ?
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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:
. . . $\displaystyle \frac{\sin x\cos x}{\sin x} + \frac{1}{\sin x} \;= \;\cos x + \csc x$
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**
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?