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# Angle between two lines watch

1. If I have two curves (say x^2 and 1-x^2) and I want to find the angle between them at the points of their interception, how would I go about doing it?

I have equated both and found their points of interception, and differentiated them both to find the gradient at the points of interception. And I know that the gradient is = tan theta, where theta is the angle between the tangent to the curve at that point and the x-axis.
But now Im not sure how to go about finding thr angle *between* the curves?? Is it just the angle between the two tangent lines at that point of interception?
2. (Original post by IDontKnowReally)
If I have two curves (say x^2 and 1-x^2) and I want to find the angle between them at the points of their interception, how would I go about doing it?

I have equated both and found their points of interception, and differentiated them both to find the gradient at the points of interception. And I know that the gradient is = tan theta, where theta is the angle between the tangent to the curve at that point and the x-axis.
But now Im not sure how to go about finding thr angle *between* the curves?? Is it just the angle between the two tangent lines at that point of interception?
First thing u want to do is draw a diagram. Then post it here and we will try to make sense of the situation. If u could mark the tangents of the graphs at the point of intersection that would be helpful.

(I need a visual aid as i cant draw the graphs myself right now)
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3. if you imagine the two tangents making a letter X, the angle you need is the angle between the branches of the X. so if one tangent angle was 82°
and the other was 59° from the horizontal then the angle between is 23°
4. (Original post by the bear)
if you imagine the two tangents making a letter X, the angle you need is the angle between the branches of the X. so if one tangent angle was 82°
and the other was 59° from the horizontal then the angle between is 23°
WHy would you subtract and not add? if the angles are both towards the horizontal
5. (Original post by IDontKnowReally)
WHy would you subtract and not add? because if the angles are both towards the horizontal
if two arrows are sticking into the same point on the ground: one is at 80 degrees to the ground, the other at 50 degrees to the ground... the angle between the arrows is 30 degrees.
6. (Original post by the bear)
if two arrows are sticking into the same point on the ground: one is at 80 degrees to the ground, the other at 50 degrees to the ground... the angle between the arrows is 30 degrees.
but how do you know its the angle from that direction? couldnt it be the angle from the opposite horizontal direction?
7. (Original post by IDontKnowReally)
but how do you know its the angle from that direction? couldnt it be the angle from the opposite horizontal direction?
typically you use the direction going to the right from the origin as your basis.
8. Find the gradients and find angles by using trigonometry. Really it's easiest to draw diagrams.
9. (Original post by TheMindGarage)
Find the gradients and find angles by using trigonometry. Really it's easiest to draw diagrams.
im just confused about which angle im actually finding tbh
10. (Original post by the bear)
typically you use the direction going to the right from the origin as your basis.
right, that makes sense thanks
11. (Original post by IDontKnowReally)
im just confused about which angle im actually finding tbh
The angle between the gradients. Or if you prefer:

(Angle between gradient 1 and horizontal)-(angle between gradient 2 and horizontal).

Draw a diagram (try to do it to scale) and use your intuition when it comes to figuring out which angle you want (the acute one or the obtuse one).

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