Arduino - Trigonometric Functions

Arduino - Trigonometric Functions

Trigonometry is the key to unlocking motion, orientation, and oscillation in your projects. Whether you’re building a robotic arm, a self-balancing robot, or creating smooth visual effects, functions like sin(), cos(), and tan() are indispensable. The Arduino platform provides these standard C++ math functions via the <cmath> library, which is included automatically in your sketches.

Core Trigonometric Functions

These functions operate on angles in radians, not degrees. The Arduino environment provides handy helper functions to convert between the two.

// Standard trigonometric functions
float sin(float rad); // Returns the sine of an angle in radians
float cos(float rad); // Returns the cosine of an angle in radians
float tan(float rad); // Returns the tangent of an angle in radians

// Inverse trigonometric functions (return angle in radians)
float asin(float value); // Returns the arc sine for a value between -1.0 and 1.0
float acos(float value); // Returns the arc cosine for a value between -1.0 and 1.0
float atan(float value); // Returns the arc tangent
float atan2(float y, float x); // A more robust arc tangent, often used for converting coordinates to an angle

// Arduino-specific angle conversion helpers
float radians(float deg); // Converts degrees to radians
double degrees(double rad); // Converts radians to degrees

Pro-Tip: float vs. double

On many classic Arduino boards (like the UNO, Nano, Mega, based on AVR microcontrollers), the double data type is a 32-bit floating-point number, exactly the same as float. Using double provides no extra precision and can be misleading. For these boards, it’s best practice to stick with float. On more powerful 32-bit boards (like the Arduino Due, ESP32, or MKR series), double provides true 64-bit precision.

Practical Example: The “Breathing” LED

Let’s use the sin() function to create a smooth, organic pulsing effect on an LED. A sine wave naturally oscillates between -1.0 and 1.0. We can scale this value to control the brightness of an LED connected to a PWM pin.

constexpr int LED_PIN = 9; // A PWM-capable pin is required (e.g., 3, 5, 6, 9, 10, 11 on UNO)
float angle = 0.0; // The current angle for the sine function, in radians
float increment = 0.02; // How fast the angle changes; controls the breathing speed

void setup() {
  // We don't need to initialize the pin for analogWrite, but it's good practice.
  pinMode(LED_PIN, OUTPUT);
  Serial.begin(9600); // For optional debugging
}

void loop() {
  // 1. Calculate the sine value. It will oscillate between -1.0 and 1.0.
  float sinValue = sin(angle);

  // 2. Map the sine value to the LED brightness range (0-255).
  // The map() function in Arduino works with integers, so we'll do it manually for floats.
  // First, shift the range from [-1.0, 1.0] to [0.0, 2.0]
  float shiftedValue = sinValue + 1.0;
  // Next, scale it to the [0, 255] range for PWM
  int brightness = (int)(shiftedValue * 127.5);

  // 3. Set the LED brightness
  analogWrite(LED_PIN, brightness);

  // 4. Increment the angle for the next loop iteration to create the animation
  angle += increment;

  // Optional: Print values to the Serial Plotter to visualize the wave!
  // Serial.println(brightness);

  delay(10); // A small delay to control the animation speed
}

Real-World Application Scenarios

• Robotics: Calculating the (X, Y) position of a robotic arm’s gripper based on the angles of its joints (known as forward kinematics). pos_x = L1 * cos(angle1) + L2 * cos(angle1 + angle2);
• Navigation: Using atan2(y_diff, x_diff) to calculate the heading (angle) your robot needs to travel to reach a target coordinate.
• Data Visualization: Creating circular or wave-like patterns on an LED matrix or a graphical display.
• Audio Synthesis: Generating simple sound waves by outputting sine values to a DAC (Digital-to-Analog Converter).

Further Learning

To better understand these concepts, try visualizing them! Use the Arduino IDE’s Serial Plotter (Tools > Serial Plotter) with the example code above (uncomment the Serial.println line). It will draw the brightness value over time, revealing the smooth sine wave.