What is the angle made by the curves $y^2=\frac {2x}{\pi},y=\sin(x) $ at point of intersection other than origin . Now I know one is parabola other is sine curve . I also know that they intersect at $(0,0), (\frac {\pi}{2},1) $ .The subtended angle is also angle between their tangents. So derivatives are $\frac {1}{\pi.y},\cos (x) $. but what do I do next substitute points?. Now I am lost.
Angle subtended by two curves.
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calculus
derivatives
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0$\tan\theta=|\dfrac{m_1-m_2}{1+m_1m_2}|$ where $m$ is slop. – 2017-01-24
1 Answers
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Hint: It is known that if two curves $f_1 (x) $ and $f_2 (x) $ intercept at $P (x_0, y_0) $ then the angle between then can be found as $$\tan \phi =\frac {f_2'(x_0)-f_1'(x_0)}{1+f_1'(x_0)f_2'(x_0)} $$ Hope this hint helps.
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0Oh so you could apply it for any curve I thought it was only for lines . – 2017-01-24