When Will I Use Trigonometry?
You've asked your math teacher. Now get the answer. Trigonometry (SOH CAH TOA) is the foundation of every robot's movement.
“When Will I Use Trigonometry?”
It is the most common whine in high school math class. “Why do I need to know Sine and Cosine? I’m never going to calculate the height of a flagpole in real life.”
You’re right. You won’t calculate flagpoles. But if you want to build a PS5, a Drone, a self-driving Tesla, or a BattleBot, Trigonometry is Oxygen. You cannot move a robot without SOH CAH TOA.
The Holonomic Drive Problem
Modern robots use Mecanum Wheels. They can move Forward, Sideways, and Diagonal. The Driver pushes the joystick 45 degrees to the right. How does the robot know what to do?
The robot brain receives:
Stick X= 0.7Stick Y= 0.7
It has to calculate the hypotenuse (Speed) and the angle (Direction).
- Magnitude (Speed): $$Speed = \sqrt{x^2 + y^2}$$ (Pythagoras).
- Angle (Direction): $$Angle = \arctan(y / x)$$ (Tangent).
The robot calculates this 50 times a second. If the math is wrong, the robot crashes.
Shooting at a Target
Your robot has a camera. It sees the goal.
- “The goal is 100 pixels to the right of center.”
- “The goal is 40 pixels up.”
How many degrees do I turn the turret? This is a triangle.
- Adjacent: Focal Length of Camera.
- Opposite: Pixel Offset.
- Formula: $$Angle = \arctan(Opposite / Adjacent)$$
Every “Aimbot” in every video game runs this calculation every frame.
Inverse Kinematics (Robot Arms)
You tell the robot: “Move the claw to coordinate (X=10, Y=20).” The robot has a shoulder joint and an elbow joint. It has to figure out: “What angle should I set the Shoulder Servo and Elbow Servo to reach that point?” This creates a triangle where the arm segments are the sides. We use the Law of Cosines to solve it.
Conclusion
Trigonometry isn’t abstract math. It is the language of physical space. It translates “Where I am” to “Where I want to be.” So pay attention in Pre-Calc. Your robot’s accuracy depends on it.