# Tangent lines of trigonometric functions

#### Petrus

##### Well-known member
Hello,
I got problem with A homework
"find an equation of the tangent line to curve at the given point.
$y=sec(x)$. $(pi/3,2)$
progress:
$y'=sec(x)tan(x)$. So basicly that sec(x) dont say me much so i rewrite it as $1/cos(x)$
$y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to calculate the slope.
i get that the slope is $m=2•sqrt(3)$ and now we use the tangent equation $y-y1=m(x-x1)$
So we got $y-2=2sqrt(3)(x-pi/3)$ and i basicly answer $y=2sqrt(3)(x-pi/3)+2$
Is this correct? I am sure i am thinking correct but not 100%

Last edited:

#### Fantini

MHB Math Helper
Re: Tangent of trigonometric functions

Yes, you are correct! I assume your last expression was

$$y = 2 \sqrt{3} \left( x - \frac{\pi}{3} \right) +2.$$

#### Petrus

##### Well-known member
Re: Tangent of trigonometric functions

Yes, you are correct! I assume your last expression was

$$y = 2 \sqrt{3} \left( x - \frac{\pi}{3} \right) +2.$$
Yes Thanks for the fast responed!

#### Fantini

MHB Math Helper
Re: Tangent of trigonometric functions

You are welcome! Keep on the right track, focusing on the concepts.

#### MarkFL

Staff member
Re: Tangent of trigonometric functions

Hello,
I got problem with A homework
"find an equation of the tangent line to curve at the given point.
$y=sec(x)$. $(pi/3,2)$
progress:
$y'=sec(x)tan(x)$. So basicly that sec(x) dont say me much so i rewrite it as $1/cos(x)$
$y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to calculate the slope.
i get that the slope is $m=2•sqrt(3)$ and now we use the tangent equation $y-y1=m(x-x1)$
So we got $y-2=2sqrt(3)(x-pi/3)$ and i basicly answer $y=2sqrt(3)(x-pi/3)+2$
Is this correct? I am sure i am thinking correct but not 100%
Hello Petrus,

Great job in presenting the problem and showing your progress! This is what we like to see.

In order to help you improve the look of your presentation, I want to offer you some tips on using $\LaTeX$.

For trigonometric (or other) functions precede them with a backslash, e.g.:

y=\sec(x) will produce $y=\sec(x)$

For special characters like the symbol for the Greek letter pi, precede this also with a backslash:

\pi will produce $\pi$

To express a fraction, use the \frac{}{} command:

\frac{\pi}{3} will produce $\frac{\pi}{3}$

To make the fraction larger, use either of the following:

\dfrac{\pi}{3} will produce $\dfrac{\pi}{3}$

\displaystyle \frac{\pi}{3} will produce $\displaystyle \frac{\pi}{3}$

Using \displaystyle will make all fractions, integrals, sums, etc. look better in your entire expression.

To enclose a composite expression containing "tall" expressions within parentheses, use \left( \right) and the parentheses will be automatically generated to be tall enough to enclose the expression:

\displaystyle \left(\frac{\pi}{3},2 \right) will produce $\displaystyle \left(\frac{\pi}{3},2 \right)$

To produce the "dot" multiplication symbol use the command \cdot, for example:

\displaystyle y'=\frac{1}{\cos(x)}\cdot\tan(x) will produce $\displaystyle y'=\frac{1}{\cos(x)}\cdot\tan(x)$

To produce the square root symbol, use the command \sqrt{}, e.g.:

m=2\cdot\sqrt{3} will produce $m=2\cdot\sqrt{3}$

To use subscripts, use the underscore character, for example:

y-y_1=m(x-x_1) will produce $y-y_1=m(x-x_1)$

As a last note, if you see a nice expression written in $\LaTeX$ by someone else, and you wish to see the code they have used, right-click on the expression, and on the pop-up menu, choose Show Math As and TeX Commands and a window will pop up showing you the commands used to produce the expression.

Happy TeXing!