Understanding Trigonometry with DIY Projects – Sin, Cos, Tan & the Unit Circle

 

Mathematics often feels like a set of rules to memorize but what if we could see and touch the concepts?

In this article, we’ll revisit our conversation about trigonometry and transform it into a fun, hands-on learning experience using DIY models.

By the end, you’ll understand:

• Why sin, cos, and tan exist as separate names

• How they work in right-angled and general triangles

• What the unit circle is and why we need it

• Simple DIY projects to demonstrate these ideas

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Sin, Cos, and Tan – Why Different Names?

At first glance, sin, cos, and tan are just ratios of sides of a triangle. Why then do we need three different names?

The answer is perspective:

• Sin θ = Opposite ÷ Hypotenuse (measures vertical rise)

• Cos θ = Adjacent ÷ Hypotenuse (measures horizontal run)

• Tan θ = Opposite ÷ Adjacent (compares rise vs. run)

Even though they are ratios, they highlight different relationships. Engineers, architects, and scientists pick the one that makes calculations easiest.

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Are They Only for Right Triangles?

A common doubt: “Are sin, cos, and tan only for right-angled triangles?”

👉 In school, we first define them using right triangles.
But with the unit circle, trigonometric functions extend to all angles (0°–360° and beyond).

That’s why sin, cos, and tan are not restricted — they are universal functions used in physics, navigation, astronomy, and computer graphics.

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The Unit Circle – Why Do We Need It?

The unit circle is a circle with radius = 1, centered at the origin.

It helps us:

1. Extend trigonometry to any angle, not just 0°–90°

2. Understand positive and negative values of sin/cos in different quadrants

3. Visualize periodicity (trig functions repeat every 360°)

4. Solve real-world problems involving rotation and waves

Without the unit circle, trigonometry would remain stuck inside a single triangle. With it, the subject opens up to infinite applications.

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DIY Trigonometry Projects

Let’s bring these concepts to life with simple models you can build at home.

1. Right Triangle Model

• Make a right triangle with popsicle sticks.

• Color the opposite, adjacent, and hypotenuse sides differently.

• Mark an angle θ and label sin θ, cos θ, and tan θ.

• This model shows the basic definitions.

2. Unit Circle Model

• Draw a circle of radius 1 on cardboard.

• Fix a rotating stick at the center with a paper fastener.

• Drop perpendiculars to axes to show sin θ (y-value) and cos θ (x-value).

• Rotate the stick to see how values change with angle.

3. Real-Life Applications

• Ladder against wall: tan θ = height ÷ base

• Building height from shadow: tan θ = height ÷ shadow

• Ramp slope for toy car: sin θ = rise ÷ slope

These models make math visible, measurable, and fun.

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Conclusion

Our conversation showed that math doesn’t have to stay on paper  it can be built, tested, and experienced.

• Sin, cos, tan are not just abstract formulas but meaningful ratios.

• The unit circle gives them life beyond triangles.

• DIY projects make learning interactive and memorable.

So, next time you wonder “Why do we need trigonometry?” pick up a few popsicle sticks and paper. You’ll see math all around you: in ladders, shadows, ramps, and even the way planets move.

• Trigonometry isn’t just about numbers   it’s a way of understanding the world.

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LED Blinking with Arduino – First Step into the World of Electronics

 

If you are just starting your journey with Arduino and robotics, the very first project you should try is the LED Blinking Project. It’s simple, fun, and acts as the “Hello World” of the Arduino world. By the end of this project, you’ll understand how to connect basic components, write simple Arduino code, and upload it to your board.

Components Required

• 1 × Arduino UNO (or any compatible board)

• 1 × LED (any color)

• 1 × Resistor (220Ω or 330Ω)

• Jumper wires

• Breadboard

• USB cable to connect Arduino to your computer

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Circuit Diagram

The circuit is very simple:

• Connect the positive leg (anode) of the LED to digital pin 13 of the Arduino (or any other digital pin).

• Connect the negative leg (cathode) of the LED to one end of the resistor.

• Connect the other end of the resistor to GND (ground) of the Arduino.

 This ensures the LED is protected and doesn’t burn out.

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Arduino Code

// LED Blinking with Arduino
int ledPin = 13; // Pin where LED is connected

void setup() {
  pinMode(ledPin, OUTPUT); // Set pin as output
}

void loop() {
  digitalWrite(ledPin, HIGH); // Turn LED ON
  delay(1000);                // Wait for 1 second
  digitalWrite(ledPin, LOW);  // Turn LED OFF
  delay(1000);                // Wait for 1 second
}

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How the Code Works

1. pinMode(ledPin, OUTPUT); → tells Arduino that pin 13 will send out signals (output).

2. digitalWrite(ledPin, HIGH); → sends 5V to the pin, turning the LED ON.

3. delay(1000); → waits for 1000 milliseconds (1 second).

4. digitalWrite(ledPin, LOW); → cuts the power, turning the LED OFF.

5. The loop() keeps repeating forever, making the LED blink continuously.

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Output

Once you upload the code, the LED will blink ON for 1 second and OFF for 1 second, repeatedly. You can experiment by:

• Changing the delay time (e.g., delay(500); for half a second).

• Connecting more LEDs to different pins.

• Creating patterns like SOS signals or traffic lights.

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Applications

Though it’s a very simple project, LED blinking is the foundation for many advanced projects like:

• Traffic light systems

• Home automation (indicator LEDs)

• Robotics (status lights)

• Signal testing in circuits

Obstacle Avoiding Robot DIY Project | Arduino Robotics for Beginners

Robotics is one of the most exciting fields in DIY electronics. Among beginner-friendly projects, the Obstacle Avoiding Robot is a great choice because it combines sensors, motors, and Arduino programming into one fun build. In this post, we’ll go step by step to make your own robot that can detect and avoid obstacles automatically.

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Materials Required

To build this project, you’ll need:

• Arduino Uno board

• Ultrasonic sensor (HC-SR04)

• Motor driver module (L298N)

• Two DC geared motors with wheels

• Robot chassis (or simple wooden/plywood board)

• Caster wheel (for balance)

• Jumper wires & battery pack (9V or 12V)

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Circuit Connection

1. Connect the ultrasonic sensor to the Arduino:

   • VCC → 5V

   • GND → GND

   • Trig → Pin 9

   • Echo → Pin 10

2. Connect the L298N motor driver to the Arduino:

   • IN1 → Pin 2

   • IN2 → Pin 3

   • IN3 → Pin 4

   • IN4 → Pin 5

   • Motor A and B to the left and right motors

3. Power the motor driver with your battery pack, and connect Arduino to the same ground.

Arduino Code Example

#define trigPin 9

#define echoPin 10

#define motor1A 2

#define motor1B 3

#define motor2A 4

#define motor2B 5

void setup() {

  pinMode(trigPin, OUTPUT);

  pinMode(echoPin, INPUT);

  pinMode(motor1A, OUTPUT);

  pinMode(motor1B, OUTPUT);

  pinMode(motor2A, OUTPUT);

  pinMode(motor2B, OUTPUT);

  Serial.begin(9600);

}

void loop() {

  long duration, distance;

  digitalWrite(trigPin, LOW);

  delayMicroseconds(2);

  digitalWrite(trigPin, HIGH);

  delayMicroseconds(10);

  digitalWrite(trigPin, LOW);

  duration = pulseIn(echoPin, HIGH);

  distance = duration * 0.034 / 2;

  if (distance < 20) { // If obstacle detected

    stopMotors();

    delay(500);

    turnRight();

    delay(600);

  } else {

    moveForward();

  }

}

void moveForward() {

  digitalWrite(motor1A, HIGH);

  digitalWrite(motor1B, LOW);

  digitalWrite(motor2A, HIGH);

  digitalWrite(motor2B, LOW);

}

void stopMotors() {

  digitalWrite(motor1A, LOW);

  digitalWrite(motor1B, LOW);

  digitalWrite(motor2A, LOW);

  digitalWrite(motor2B, LOW);

}

void turnRight() {

  digitalWrite(motor1A, HIGH);

  digitalWrite(motor1B, LOW);

  digitalWrite(motor2A, LOW);

  digitalWrite(motor2B, HIGH);

}

Working Principle

The ultrasonic sensor constantly measures the distance ahead. If it detects an obstacle closer than 20 cm, the Arduino commands the motors to stop and then turn the robot to avoid the object. If no obstacle is detected, the robot keeps moving forward.

Results

Once assembled and programmed, your robot will roam around while avoiding walls, boxes, and other obstacles. It’s an exciting beginner’s robotics project that gives you hands-on experience with sensors, motor control, and Arduino coding.

With this project, you’ll learn how to combine hardware and software to create an intelligent machine. Try building it, experiment with code, and share your version with your friends!