Parametric equations and polar coordinates

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$x(t) = t + 1$ and $y(t) = t^2$ . Tap the point where the curve is at $t = 1$ .
$x(t) = 4t + 4$ and $y(t) = t - 1$ . At what time $t$ does the point have $x = 8$ ?
$x = t + 6$ and $y = t^2$ . Write $y$ in terms of $x$ .
$x = 3t$ and $y = 4t + 9$ . Write $y$ in terms of $x$ .
What curve do $x = 5\cos t$ and $y = 5\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 5 centered at the origin
2. A line
3. A circle of radius $25$
What curve do $x = 2\cos t$ and $y = 2\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 2 centered at the origin
2. A line
3. A circle of radius $4$
What curve do $x = 9\cos t$ and $y = 9\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 9 centered at the origin
2. A line
3. A circle of radius $81$
What curve do $x = 7\cos t$ and $y = 7\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 7 centered at the origin
2. A line
3. A circle of radius $49$
What curve do $x = 3\cos t$ and $y = 3\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 3 centered at the origin
2. A line
3. A circle of radius $9$
What curve do $x = 8\cos t$ and $y = 8\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 8 centered at the origin
2. A line
3. A circle of radius $64$
What curve do $x = 4\cos t$ and $y = 4\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 4 centered at the origin
2. A line
3. A circle of radius $16$
What curve do $x = 6\cos t$ and $y = 6\sin t$ draw, for $0 \le t < 2\pi$ ?
1. A circle of radius 6 centered at the origin
2. A line
3. A circle of radius $36$
The ellipse $x = 3\cos t$ , $y = 4\sin t$ reaches $x$ -values from $-c$ to $c$ . What is $c$ ?
A point moves on $x = 7\sin t$ , $y = 7\cos t$ . At $t = 0$ it is at $(0, 7)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 5\sin t$ , $y = 5\cos t$ . At $t = 0$ it is at $(0, 5)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 9\sin t$ , $y = 9\cos t$ . At $t = 0$ it is at $(0, 9)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 4\sin t$ , $y = 4\cos t$ . At $t = 0$ it is at $(0, 4)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 3\sin t$ , $y = 3\cos t$ . At $t = 0$ it is at $(0, 3)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 6\sin t$ , $y = 6\cos t$ . At $t = 0$ it is at $(0, 6)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 2\sin t$ , $y = 2\cos t$ . At $t = 0$ it is at $(0, 2)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 8\sin t$ , $y = 8\cos t$ . At $t = 0$ it is at $(0, 8)$ . Which way does it go as $t$ increases?
1. Clockwise
2. Counterclockwise
3. Along a straight line
A point moves on $x = 8\cos(4t)$ , $y = 8\sin(4t)$ . How long does one full turn take?
Tap the point with polar coordinates $\left(4, \frac{3 \pi}{2}\right)$ .
What is the graph of the polar equation $r = 5$ ?
1. A circle of radius 5 centered at the origin
2. A line through the origin
3. The vertical line $x = 5$
What is the graph of the polar equation $r = 7$ ?
1. A circle of radius 7 centered at the origin
2. A line through the origin
3. The vertical line $x = 7$
What is the graph of the polar equation $r = 8$ ?
1. A circle of radius 8 centered at the origin
2. A line through the origin
3. The vertical line $x = 8$
What is the graph of the polar equation $r = 4$ ?
1. A circle of radius 4 centered at the origin
2. A line through the origin
3. The vertical line $x = 4$
What is the graph of the polar equation $r = 2$ ?
1. A circle of radius 2 centered at the origin
2. A line through the origin
3. The vertical line $x = 2$
What is the graph of the polar equation $r = 3$ ?
1. A circle of radius 3 centered at the origin
2. A line through the origin
3. The vertical line $x = 3$
What is the graph of the polar equation $r = 6$ ?
1. A circle of radius 6 centered at the origin
2. A line through the origin
3. The vertical line $x = 6$
What is the graph of the polar equation $r = 9$ ?
1. A circle of radius 9 centered at the origin
2. A line through the origin
3. The vertical line $x = 9$
The polar equation $r = 12\sin\theta$ is a circle. In rectangular coordinates, it is $x^2 + y^2 = 12y$ . What is the $y$ -coordinate of its center?
The polar equation $\theta =\frac{\pi}{6}$ is a line through the origin. What is its slope?
Find the exact modulus $|z|$ of $z = 3 - 8i$ .
Find the argument of $z = -6 + 1i$ , between $0^\circ$ and $360^\circ$ , to 1 decimal place.
Write $z = 3\left(\cos 120^\circ + i\sin 120^\circ\right)$ in the form $a + bi$ (exact).
Use De Moivre's theorem to write $\left(\cos 60^\circ + i\sin 60^\circ\right)^{ 2 }$ in the form $a + bi$ (exact).
What is the distance between 4 + 3i and -4 + -6i in the complex plane?
What is the real part of the midpoint of 5 + -7i and -2 + -7i?
What is the modulus |7 + 8i|, the distance from 7 + 8i to 0?

Answers

$(2, 1)$
$1$
$\left(x - 6\right)^{2}$
$\frac{4 x}{3} + 9$
A circle of radius 5 centered at the origin
$3$
Clockwise
$\frac{\pi}{2}$
$(0, -4)$
A circle of radius 5 centered at the origin
$6$
$\frac{\sqrt{3}}{3}$
$\sqrt{73}$
$- \frac{180 \tan^{-1}{\left(\frac{1}{6} \right)}}{\pi} + 180$
$- \frac{3}{2} + \frac{3 \sqrt{3} i}{2}$
$- \frac{1}{2} + \frac{\sqrt{3} i}{2}$
$\sqrt{145}$
$\frac{3}{2}$
$\sqrt{113}$