Vector Vision Exit Ticket Vector Vision
Exit Ticket: Unit 1.1
Sector: Plotting & Conversion
Operator Name
Date
01 Target Acquisition
Plot the following coordinate on the radar grid:
\( P(3, \frac{5\pi}{6}) \)
Mark the point clearly and show the counter-clockwise rotation from the polar axis.
0 π/2 π 3π/2
02 Signal Translation
Polar → Rectangular:
\( r = 4, \theta = \frac{4\pi}{3} \). Show work:
Rectangular → Polar:
\( (x, y) = (-3, 3) \). Find \( (r, \theta) \):
03 Identity Verification
Find two other pairs of polar coordinates for the point \( (2, 45^\circ) \):
r < 0:
θ < 0:
Pre-Calculus Radar Station // Sector 1.1 Scanning Complete
Curve Chaos Exit Ticket Curved Signal
Exit Ticket: Unit 1.2
Sector: Limacons & Rose Curves
Operator Name
Date
01 Waveform Classification
Match the polar equations to their curve types. Write A, B, or C.
r = 3 sin(2θ)
A. Limaçon (inner loop)
r = 2 - 2 cos(θ)
B. Rose Curve (4 petals)
r = 1 + 3 sin(θ)
C. Cardioid
02 Visual Signature
For the curve \( r = 4 \cos(3\theta) \):
Number of petals:
Petal length:
Type of symmetry:
Sketch Reference
03 Interference Check
Compare \( r = 2 + \sin(\theta) \) and \( r = 1 + 2 \sin(\theta) \). Which one has an inner loop and why?
Response:
Pre-Calculus Radar Station // Sector 1.2 Signal Analyzed
Complex Polar Exit Ticket Complex Frequency
Exit Ticket: Unit 1.3
Sector: Complex Numbers in Polar Form
Operator Name
Date
01 Phase Analysis
Write the complex number \( z = \sqrt{3} + i \) in polar form \( r(\cos \theta + i \sin \theta) \). Provide the modulus \( r \) and the argument \( \theta \) first.
Modulus (\( r \)):
Argument (\( \theta \)):
Final Polar Expression:
z =
02 Signal Modulation
Multiply the complex numbers and state the result in polar form:
\( z_1 = 3(\cos \frac{\pi}{4} + i \sin \frac{\pi}{4}) \)
Product Calculation:
03 Amplification Check
Evaluate \( [2(\cos 30^\circ + i \sin 30^\circ)]^3 \). Write your answer in rectangular form \( a + bi \).
Pre-Calculus Radar Station // Sector 1.3 Power Levels Normal
Polar Mastery Answer Key Radar Ops Key
Unit: Polar Coordinates // Teacher Reference
1.1 Vector Vision
01. Plotting
\( P(3, \frac{5\pi}{6}) \): 3rd circle, \( 150^\circ \) (Q2 radial line).
02. Translation
Polar → Rect: \( (-2, -2\sqrt{3}) \)
Rect → Polar: \( (3\sqrt{2}, \frac{3\pi}{4}) \)
03. Verification
\( r < 0 \): \( (-2, 225^\circ) \)
1.2 Curved Signal
01. Classification
1: B // 2: C // 3: A
02. Visual Signature
Petals: 3 // Length: 4 // Sym: Polar Axis
03. Check
\( r = 1 + 2 \sin(\theta) \) has loop because \( |a/b| < 1 \) (specifically \( 1 < 2 \)).
1.3 Complex Frequency
01. Phase Analysis
\( r = 2 \), \( \theta = 30^\circ \) or \( \pi/6 \)
02. Signal Modulation
Moduli: \( 3 \cdot 2 = 6 \). Angles: \( \pi/4 + \pi/2 = 3\pi/4 \).
\( 6(\cos \frac{3\pi}{4} + i \sin \frac{3\pi}{4}) \)
03. Amplification
\( 2^3 (\cos 90^\circ + i \sin 90^\circ) = 8(0 + i) = 8i \).
Answer: \( 0 + 8i \)
Facilitation Notes
Check that students are plotting the angle first, then the radius.
For Limacons, emphasize the ratio \( a/b \) for loop identification.
In Complex form, verify students identify the correct quadrant for \( \theta \).
Pre-Calculus Radar Station // System Key All Sectors Verified
