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Calculus :(
Can someone please explain to me how you find an equation of a tangent line at a given point?
For example, how would you find the tangent line to y=tan(x) at the point (pi/4, 1)? I know the answer is y=2x+1-.5(pi) but I don't understand how you get that from y=tan(x). I know it has something to do with taking the derivative but the derivative of tan(x) is sec^2(x), so how do you get the tanget line from that?
I'm sorry if this is confusing. I think if you understand calculus, you'll get what I'm asking. I just need someone to explain to me how you get the tangent line at the given point. I would really appreciate it. :) Thanks!
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First of all, you're right in that you need to take the derivative of the equation. That gives you the gradient of the tangent.
So, in your example, you have the line y=tan(x), which has the derivative sec^2(x). Now, at the point (pi/4, 1), sec^2(x) is 2, so you know that the gradient of the tangent at that point is 2.
Now, substitute the values into the general form y=mx + c.
1 = 2 * pi/4 + c
c = 1 - pi/2
and that gives us the answer that you have, which is y = 2x + 1 - pi/2.
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