Consider the curve x = et-5 cos t, y = et-5 sin t, 0

Q: Find  the slope of the curve y=cos((pi tanx)/6) at the point where x=pi/2.

A: given,  y=cos(pi tanx)6  at x=π2

Q: Sketch the curve r = 3 sin(2θ)

A: To sketch the curve r = 3 sin(2θ) It's amplitude lies between -3 to 3  At θ = 45°, sin(2θ) =…

Q: 3. If y = 4cos x + sin 2x, what is the slope of the curve when x = 2 radians? A.-2.21 B.-4.94…

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Q: Sketch the graph of r = 1–2 cos 0. Find tangents at the pole, all vertical and horizontal tangents.

A: Consider the given equation of graph.

Q: Find the Cartesian equation of the image of the line x = 2 under the mappingz → sin(z). Sketch…

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Q: Sketch the curve r= cos 2θ

A: Symmetric test for polar coordinates r=f(θ): If f(θ)=f(-θ) then graph is symmetric about polar…