The slope of the tangent to the curve x = 2 sin3θ, y = 3 cos3θ at θ = pi/4 is ______.

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The slope of the tangent to the curve x = 2 sin3$\theta$, y = 3 cos3$\theta$ at $\theta$ = pi/4 is bbunderline(-$\frac{3}{2}$). Explanation: x = 2 sin3$\theta$, and y = 3 cos3$\theta$ `therefore dx/(d theta) = 6 sin^2 theta cos theta and dy/(d theta) = -9 cos^2 theta sin theta dy/dx = (dy/(d theta))/(dx/(d theta)) = (-9 cos^2 theta sin theta)/(6 sin^2 theta cos theta (-3)/2 cot theta $\therefore$ Slope of tangent at theta = pi/4 "is" (dy/dx)_(theta = pi/4) = (-3)/2 cot pi /4 = (-3)/2`.

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