1. function question

Let f and g be the functions defined by f(x)=sinx and g(x)=cosx. for which of the following values of a is the tangent line to f at x=a parallel to the tangent line to g at x=a? The answer is 3pi/4 but I dont understand how to get to that...

2. Parallel lines have the same slope.
The derivative determines the slope, so $f'(x) = g'(x)$.
So for what x does $\cos (x) = - \sin (x)$?

3. what do I use to solve that though? Is there a trig rule that I'm not thinking of that is needed to solve?

4. can anybody point out how I go about solving that?

5. Originally Posted by jst706
can anybody point out how I go about solving that?
If you really can't see the solution:

Write this as
$sin(x) = -cos(x)$

$\frac{sin(x)}{cos(x)} = -1$

$tan(x) = -1$

Can you take it from here?

-Dan

6. unfortunately....no...I don't know how to get the x separated from the tan..and then get the pi answer, could you show me and then tell me what these specific rules are called so I can go look them up?

7. Originally Posted by jst706
unfortunately....no...I don't know how to get the x separated from the tan..and then get the pi answer, could you show me and then tell me what these specific rules are called so I can go look them up?
How can you be given such a question and not have been told how to get the answers??

Try this site for some basic definitions.

-Dan

8. thanks for the site...it was helpful...but tan(x)=-1 so, according to that site x=-45...when converted to radians its says 45 degrees is pi/4 so how would they get 3pi/4? thanks for your help.

9. Originally Posted by jst706
thanks for the site...it was helpful...but tan(x)=-1 so, according to that site x=-45...when converted to radians its says 45 degrees is pi/4 so how would they get 3pi/4? thanks for your help.
Hello,

the solution of the equation tan(x) = -1 is not a single value but a set of numbers. There is a main interval where you can find the first solution: $\left(-\frac{\pi}{2}, \frac{\pi}{2} \right)$

$\tan(x)=-1~\implies~x=-\frac{\pi}{4}$. All other solutions are produced by adding multiples of $\pi$. That means the next solution is:
$x = -\frac{\pi}{4}+\pi=-\frac{3 \pi}{4}$

I've attached a diagram of the functions f(x) = tan(x) and the line y = -1. The x-coordinate of the intersection points are the solutions of your equation.
Attached Thumbnails
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