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C3 Trig

Hey, I'm totally stuck on this question and it's only the second of 35-its going to be a loong half term:frown: can anybody help?

'The lines l1 an d l2, with equations y=2x and 3y=x-1 respectively, are drawn on the same set of axes. Given that the scales are the same on both axes and that the angles l1 and l2 make with the x-axis are A and B respectively,
a) write down the value of tanA and value of tanB;
b) without using your calculator, work out the acute angle between l1 and l2.'

I know that a) is tanA=2 and tanB=1/3 and I realise these are the gradients of the lines, could anyone explain why this is the answer though?
b) 45 degrees, however I have no idea where this came from of how to get to this??
Original post by Rbutton
...


For (a), consider the definition of tan⁡θ \tan \theta and the definition of a gradient.
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Rbutton
OP
13
Original post by lazy_fish
For (a), consider the definition of tan⁡θ \tan \theta and the definition of a gradient.


So it's because the gradient is the tangent to the x-axis?
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Avatar for davros
davros
16
Original post by Rbutton
So it's because the gradient is the tangent to the x-axis?


It's not the "tangent to the x axis" - that doesn't make sense!

Draw yourself a picture of some random straight line that intersects the x-axis.

What do you do to work out the gradient of that straight line?
What do you do to work out the tangent of the angle that the line makes with the x-axis?

:smile:

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