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Magazine Problem 17
Sketch a graph of the polar equation, and express the equation in rectangular coordinates. $$r=2$$
Problem 18
A pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. $$x=\cos 2 t, \quad y=\sin 2 t$$
Problem 18
Sketch a graph of the polar equation, and express the equation in rectangular coordinates. $$r=-1$$
Problem 18
Sketch the complex number \(z\) and its complex conjugate \(z\) on the same complex plane. $$z=-5+6 i$$
Problem 19
A pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. $$x=\sec t, \quad y=\tan t, \quad 0 \leq t<\pi / 2$$
Problem 19
Sketch \(z_{1}, z_{2}, z_{1}+z_{2},\) and \(z_{1} z_{2}\) on the same complex plane. $$z_{1}=2-i, \quad z_{2}=2+i$$
Problem 20
Sketch \(z_{1}, z_{2}, z_{1}+z_{2},\) and \(z_{1} z_{2}\) on the same complex plane. $$z_{1}=-1+i, \quad z_{2}=2-3 i$$
Problem 20
Sketch a graph of the polar equation, and express the equation in rectangular coordinates. $$\theta=5 \pi / 6$$
Problem 20
A pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. $$x=\cot t, \quad y=\csc t, \quad 0 < t < \pi$$
Problem 21
Sketch the set in the complex plane. $$\\{z=a+b i | a \leq 0, b \geq 0\\}$$
