Finding the Tangent and normal line of tan(x) at point (pi/4 , f(pi/4) )

[marco213]

Finding the Tangent and normal line of tan(x) at point (pi/4 , f(pi/4) )

Pi is confusing me deeply and I really need help... A short explaination about how to use Pi would be greatly appreciated!

 

[stapel]

Finding the Tangent and normal line of tan(x) at point (pi/4 , f(pi/4) )

Pi is confusing me deeply and I really need help... A short explaination about how to use Pi would be greatly appreciated!

Are you saying that you're working with trig functions, but that you're not familiar with the number \(\displaystyle \pi\)? :shock:

 

[pka]

Pi is confusing me deeply and I really need help... A short explaination about how to use Pi would be greatly appreciated!

Let \(\displaystyle f(x)=\tan(x)\) then \(\displaystyle f'(x)=\sec^2(x)\).

Now \(\displaystyle \cos \left( {\dfrac{\pi }{4}} \right) = \dfrac{{\sqrt 2 }}{2}\) and \(\displaystyle \sin \left( {\dfrac{\pi }{4}} \right) = \dfrac{{\sqrt 2 }}{2}\).

You now know \(\displaystyle \tan \left( {\dfrac{\pi }{4}} \right) = ?\)

You show the rest of the work.

 

[ahorn]

I got y=2x+1-pi/2 for the tangent. Is that correct?


The gradient is: \(\displaystyle sec^2(\pi/4)\\

=\frac{1}{cos^2(\pi/4)}\\
=\frac{1}{\frac{1^2}{\sqrt{2}^2}}\\

=2\)