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Magazine Problem 36
Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in \(x\) and \(y\). \(x=a \sin ^{n} t, y=b \cos ^{n} t,\) where \(a\) and \(b\) are real numbers and \(n\) is a positive integer
Problem 36
Express the following Cartesian coordinates in polar coordinates in at least two different ways. $$(-8 \sqrt{3},-8)$$
Problem 36
Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the cardioid \(r=4+4 \sin \theta\)
Problem 36
Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin. A parabola symmetric about the \(x\) -axis that passes through the point (1,-4)
Problem 37
Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the lima莽on \(r=2+\cos \theta\)
Problem 37
Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique. A circle centered at the origin with radius \(4,\) generated counterclockwise
Problem 37
Convert the following equations to Cartesian coordinates. Describe the resulting curve. $$r \cos \theta=-4$$
Problem 38
Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique. A circle centered at the origin with radius \(12,\) generated clockwise with initial point (0,12)
Problem 38
Convert the following equations to Cartesian coordinates. Describe the resulting curve. $$r=\cot \theta \csc \theta$$
Problem 39
Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique. A circle centered at (2,3) with radius \(1,\) generated counterclockwise
