Core Calculus help?

[Melissi]

Hi everyone!

I've gotten really stuck while trying to do question 7 below. It's actually not the calculus specifically that I'm not getting (the differentiation I found quite easy) but this question is asking me to find the angle between two lines. I know I could do this using vectors, so I tried doing that - but then in trying to find the vectors of the lines I got massively confused, and even when just trying to figure out the equations of lines I ended up with a massive monster of an equation which doesn't really help.

So, long story short - could anyone please have a look at this question 7(b)? Any ideas on where to start (or just generally how to solve it) would be really helpful, thanks!

[twilight]

Sketch the graph and locate points P and Q. Draw the tangent line at point P. The first derivative at point P basically gives you the gradient of the tangent line, and the gradient which is rise over run is essentially the tan of the angle between the line parallel to the x-axis (if not the x-axis itself) and the tangent line.

You can do the same for the chord of PQ, find the equation of PQ then find the gradient, then that would be the tan of the angle again. Depending on how your drawing ends up, you do something to the 2 angles that you have (either add them, subtract, add 90 degree etc I don't know I didn't draw the diagram out).

[Melissi]

Thank you very much!

[Dax]

There's actually a formula for this, tan (theta) = Abs (m1 - m2)/ (1 + m1 * m2) Abs, where Theta is the angle between the two slopes and m1 and m2 are the slopes of 2 lines in question.