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Question
The slope of the tangent to the curve x = 2 sin3θ, y = 3 cos3θ at θ = `pi/4` is ______.
Options
`3/2`
`-3/2`
`2/3`
`-2/3`
Solution
The slope of the tangent to the curve x = 2 sin3θ, y = 3 cos3θ at θ = `pi/4` is `bbunderline(-3/2)`.
Explanation:
x = 2 sin3θ, and y = 3 cos3θ
`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`
∴ Slope of tangent at `theta = pi/4 "is" (dy/dx)_(theta = pi/4) = (-3)/2 cot pi /4 = (-3)/2`.
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