If the angle made by the tangent at the point (x0, y0) on the curve [x = 12(t + t t)], [y …

Question

If the angle made by the tangent at the point (x0, y0) on the curve $$x = 12(t + \sin t\cos t)$$, $$y = 12{(1 + \sin t)^2}$$

Accepted Answer

$$\because$$ $${{dy} \over {dx}} = {{24(1 + \sin t)\cos t} \over {12(1 + \cos 2t)}} = {{1 + \sin t} \over {\cos t}} = \tan \left( {{\pi  \over 4} + {t \over 2}} \right)$$

$$\because$$ $${{dy} \over {d{x_{({x_0},{y_0})}}}} = \sqrt 3  = \tan \left( {{\pi  \over 4} + {t \over 2}} \right)$$

$$ \Rightarrow t = {\pi  \over 6}$$

So, $${y_{0\left( {at\,t = {\pi  \over 6}} \right)}} = 12{\left( {1 + \sin {\pi  \over 6}} \right)^2} = 27$$

Solutions · 1