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Homework Statement
Find the angle made by the two tangents to the curve ##x=\sin2t## and ##y=\sin(2t)\cos(2t)## at the point ##(0,0)##
Homework Equations
##\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}##
(Derivative of a parametric equation)
The Attempt at a Solution
## x = \sin(2t) = 0 ## when ## t = 0, \frac{\pi}{2}, \pi,... ##
## y=\sin(2t)\cos(2t) = 0 ## at the same values of ## t##
Taking the derivative of the parametric equations by using the formula in part two, I get ##\frac{2\cos^2(2t)-2t\sin^2t}{2\cos(2t)}## I get to plug in any value of t, so I choose ##t=\pi/2##
With that t value, I get ## \frac{2(-1^2)-2(0)}{-2}## which is equal to ##-1##
Now I'll try ##t=0##, and I get ##1##. Using ##t=\pi## I also get one. Therefore, the angle must be between -1 and 1 and be equal to ## t = 0, \frac{\pi}{2}, \pi,... ##
My answer is 0.
The correct answer is ##\frac{\pi}{2}##
Could someone please enlighten me as to my mistake? That would be highly appreciated. Thanks.
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