Polar/Parametric
Convert the polar point (2, pi/3) into a rectangular point. (Everest)
What is (1, 31/2)?
What is tan(pi)? (Everest)
What is 0?
Tommy Devito needs to win the Giants game (good luck). Malik Nabers is 50 yards downfield and 20 yards to the left. At what angle does Devito need to throw the ball and how far does the throw need to be to score the touchdown? (Cooper)
What is 21.8 degrees and 53.85 yds?
Consider the polar equation r = 3/(1+(3/2)cos(theta)). What is the eccentricity and directrix? (Scarlett)
What is 3/2 and x=2?
| -1 0 |
| 0 1 |
What does this matrix do? (Ms. Dickey)
What is reflect over the y-axis?
Write two different polar coordinates for (3, 4). (Nora)
What are (5, 53.13 degrees) and (-5, 306.87 degrees)? [others are possible]
Find tan-1(-1). (Everest)
What is -pi/4?
Let a = 4 i + 2 j+5 k and b = 6 i + j + 2 k. Find a x b. (Everest)
What is -i + 22 j - 8 k?
The shape of Arrowhead stadium is an ellipse centered at (1, 0), with a covertex at (3, 0) and a vertex at (1, 6). Write the equation in standard form of the ellipse. (Alex)
What is (x-1)2/4 + y2/36=1?
Everest is doing a backflip on skis. He spins at an angular speed of pi/6 rads/sec. How many seconds would it take him to finish a full flip? If Everest is 6ft tall (so 6ft diameter), what linear speed would his flip create? (Cooper)
What is 12 seconds and pi/2 ft/second?
Swiss Semester students are making designs in the snow. They want to make a rose with 5 petals and each petal is 5 meters long. They want it to be symmetric across the x-axis. Write a polar equation for this design. (Nora)
What is r=5cos(5(theta))?
What is stretch by 7 and up 15?
State the amplitude, period, and frequency of y=(1/2)cos(2x+pi) - (3pi)/2. (Everest)
What is (1/2), pi, and 1/pi?
Find the vertices and foci of 4x2-y2-8x-4y-16=0. (Alex)
What are V: (3, -2) and (-1, -2)
F: (1+2(5)1/2, -2) and (1-2(5)1/2, -2)?
The KC Chiefs need to downsize Arrowhead (bc Taylor Swift lost relevance) by 1/4. What is the proper dilation matrix system to apply? (Alex)
What is
x' = | 4 0 | x
y' = | 0 4 | y
Given x(t) = 4t - 1 and y(t) = (t + (1/4))/t, find the Cartesian equation as well as the domain and range of the equation. (Alex)
What is y = (x+2)/(x+1) and
D: (-infty, -1)U(-1, infty)
R: (-infty, -1)U(-1, infty)?
What are the domains and ranges of the 6 trig functions? (Nora)
What are
sin/cos: D: (-infty, infty), R: [-1, 1]
tan/cot: D: (-infty, infty) except asymp., R: (-infty, infty)
sec/cos: D: (-infty, infty) except asymp., R: (-infty, -1]U[1, infty)
A skier is skiing very quickly across a flat surface for 10ft with a drop-off, hits a paraglider and drops straight down. If the angle of depression is 40 degrees, how many feet did he fall? (Everest)
What is 8.39 feet?
You want to find a hyperbola whose asymptotes are y=(3/5)x and y = (-3/5)x. The vertices are on the y-axis. The latera recta have a length of 50/3. What is the equation for the hyperbola?
What is y2/9-x2/25=1?
To turn from Breithorn to Monte Rosa is a clockwise 30 degrees rotation. Express this as a rotation matrix. (Scarlett)
What is
| 31/2/2 1/2 |
| -1/2 31/2/2 |?
A car races around a circular track with a radius of 4, moving counterclockwise. If it takes pi to go a full lap, find a parametric representation of the track. Let the center of the track be the origin. (Alex)
What is x(t) = 4cos(2t), y(t) = 4sin(2t)?
A chairlift, on flat ground, goes up and down as you pass the posts. Your highest point is 30 m (at a post), your lowest point is 26 m (between posts). The distance between the posts is 10 m. You start at a post (30 m high). Write a sinusoidal function to represent this motion. (Nora)
What is y=cos((pi/5)x)+28?
Prove the identity 4(cos(x))4=1 + 2cos(2x)+(cos(2x))2. (Everest)
What is
1 + 2cos(2x)+(cos(2x))2 = (1+cos(2x))(1+cos(2x))
= 2(cos(x))2(2(cos(x))2)
=4(cos(x))4
You want to go to a place equidistant from Migros, Denner, and Coop. Migros is at (5, 5-(7)1/2), Denner is at (2, 9), and Cooper is at (6, 5). Find the equation of the circle containing the three stores and the center is where you are. (Scarlett)
What is (x-2)2+(y-5)2=16?
Christoff has an equation to predict weather, but he hates first degree terms. If the equation is 6x2-2y2+9x+4y=0, what should your translation be? (Scarlett)
What is x=x' - 3/4 and y = y'+1?