Mathematics, 21.07.2019 15:00 Jasonn7787
Show that the curvex = 2 cos t, y = 3 sin t cos t has two tangents at (0, 0) and find their equations.
Answers: 1
![\frac{dy}{dt} = 3[cos(t)cos(t)+sin(t)(-sin(t))]](/tpl/images/0116/0222/77ffb.png)
![\frac{dy}{dt} = 3[cos^{2} (t)-sin^{2} (t)]](/tpl/images/0116/0222/c230e.png)
![\frac{dy}{dx} = \frac{-3[cos^{2} (t)-sin^{2} (t)]}{2sin(t)}](/tpl/images/0116/0222/e923d.png)
and 
, so:
π/2
:![m_{1}= \frac{dy}{dx} = \frac{-3[cos^{2} ( \pi /2)-sin^{2} ( \pi /2)]}{2sin( \pi /2)} = \frac{3}{2}](/tpl/images/0116/0222/b274f.png)
:![m_{2}= \frac{dy}{dx} = \frac{-3[cos^{2} ( -\pi /2)-sin^{2} ( -\pi /2)]}{2sin(- \pi /2)} = -\frac{3}{2}](/tpl/images/0116/0222/bac4a.png)
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Show that the curvex = 2 cos t, y = 3 sin t cos t has two tangents at (0, 0) and find their equation...
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