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Quiz: Linear Motion, Trigonometry & Wave Math

Test your understanding of Velocity, acceleration, trigonometry, sine, cosine, and periodic wave motion with these review questions.

1. What mathematical relationship defines position update under constant velocity?

  1. pos = pos + velocity;
  2. pos = velocity * acceleration;
  3. pos = pos / deltaTime;
  4. pos = sqrt(velocity);
Show Answer

The correct answer is A. Under constant velocity, new position equals current position plus velocity on each discrete time step. Options B, C, and D do not represent kinematic position integration.

Concept Tested: Linear Motion Logic

2. Which trigonometric function calculates the ratio of the opposite side to the hypotenuse in a right triangle?

  1. sin()
  2. cos()
  3. tan()
  4. atan2()
Show Answer

The correct answer is A. Sine is the ratio of opposite side over hypotenuse. Cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

Concept Tested: Sine Function Math

3. What is the output range of the standard mathematical sin(angle) and cos(angle) functions?

  1. From 0 to 1
  2. From -1 to 1
  3. From 0 to TWO_PI
  4. From -Infinity to +Infinity
Show Answer

The correct answer is B. The sine and cosine wave functions oscillate continuously between a minimum of -1.0 and a maximum of +1.0. Options A, C, and D represent incorrect ranges.

Concept Tested: Trigonometric Range

4. To create smooth back-and-forth horizontal oscillation centered at x = 200 with an amplitude of 50 pixels, which formula is correct?

  1. x = 200 * sin(angle) + 50;
  2. x = 200 + sin(angle) * 50;
  3. x = sin(200) + angle * 50;
  4. x = (200 + angle) * sin(50);
Show Answer

The correct answer is B. Multiplying sin(angle) by the amplitude 50 produces an oscillation between -50 and +50. Adding the center offset 200 shifts the oscillation range to [150, 250]. Options B, C, and D yield incorrect movement.

Concept Tested: Oscillation Wave Math

5. Which p5.js function computes the angle (in radians) from the origin (0, 0) to any coordinate (x, y)?

  1. atan(y / x)
  2. atan2(y, x)
  3. acos(x)
  4. asin(y)
Show Answer

The correct answer is B. atan2(y, x) calculates the angle in radians to (x, y) across all four quadrants without division-by-zero errors. atan() only handles two quadrants. Options C and D find angles from single ratios.

Concept Tested: Atan2 Function

6. How do you convert polar coordinates (r, theta) to 2D Cartesian coordinates (x, y)?

  1. x = theta * cos(r); y = theta * sin(r);
  2. x = r + cos(theta); y = r + sin(theta);
  3. x = r * cos(theta); y = r * sin(theta);
  4. x = r / cos(theta); y = r / sin(theta);
Show Answer

The correct answer is C. Cartesian x is radius * cos(angle) and y is radius * sin(angle). This formula is fundamental for drawing circles, spirals, and rotational orbits. Options B, C, and D are mathematically incorrect.

Concept Tested: Polar to Cartesian Conversion

7. What visual effect is produced when two harmonic sine waves with different frequencies modulate a shape's x and y positions?

  1. A static straight line
  2. Random walk brownian motion
  3. Lissajous curve figures
  4. A square bounding box
Show Answer

The correct answer is C. When x and y positions are driven by perpendicular sinusoidal signals of differing frequencies, the resulting parametric trajectory traces elegant, looping Lissajous figures. Options B, C, and D are incorrect.

Concept Tested: Lissajous Curves

8. You want an angle variable to increment by 0.05 on every frame. Where should angle += 0.05; be placed?

  1. Inside the preload() function
  2. Inside the setup() function
  3. Inside the draw() function
  4. In the HTML index script header
Show Answer

The correct answer is C. To produce continuous animation across time, the angle must be incremented during each frame execution inside the draw() loop. Options A and B execute only once before rendering begins.

Concept Tested: Continuous Animation State

9. Why is atan2(y, x) preferred over atan(y / x) when programming an eye or turret that tracks the mouse position?

  1. atan2() returns angles in degrees instead of radians
  2. atan2() runs 10x faster on CPU hardware
  3. atan() cannot process floating-point numbers
  4. atan2() automatically handles full 360-degree four-quadrant geometry and avoids division by zero when x is 0
Show Answer

The correct answer is D. atan(y / x) fails when x = 0 (division by zero) and cannot distinguish between opposite quadrants (e.g. (+y, +x) vs (-y, -x)). atan2(y, x) takes both signs into account to return the correct angle across all four quadrants. Options B, C, and D are false.

Concept Tested: Atan2 Quadrant Analysis

10. If a wave's frequency is doubled while maintaining constant speed and amplitude, what happens to the wave on screen?

  1. The waves become twice as tall vertically
  2. The wave inverts upside down
  3. The wave stops moving completely
  4. The peaks appear twice as close together horizontally (wavelength is halved)
Show Answer

The correct answer is D. Frequency represents cycles per unit time or distance. Doubling frequency halves the spatial wavelength, packing twice as many wave crests into the same horizontal space. Amplitude controls height. Options A, C, and D are incorrect.

Concept Tested: Wave Frequency and Wavelength