ELI5: How are Sin, Cos, and Tan useful outside of geometry?

Imagine you're pushing a swing!

Sin, Cos, and Tan (we call them trigonometric functions) help us understand how things move in circles or back and forth, even if they don't look like circles at first!

• Ramps and Slides: Let's say you're building a ramp for your toy car. Cosine helps you figure out how much horizontal distance the ramp takes up compared to its length. Sine helps you figure out how high the ramp goes up compared to its length. If you want a steep ramp, Sine will be bigger!

• Sound Waves: Sound travels in waves, like ripples in a pond. Sine and Cosine can describe these waves. A louder sound has a bigger wave (bigger Sine value). This is how music players work!

• Electricity: The electricity that powers your lights and TV also flows in waves! Just like sound, Sine and Cosine can describe these waves.

• GPS: When your parents use GPS in the car, it uses trigonometry to figure out where you are. Satellites send signals, and the angles between those signals are used with Sine, Cosine, and Tangent to pinpoint your location on a map.

• Building Things: When builders design buildings or bridges, they use trigonometry to make sure everything is strong and stable. For example, they use Sine and Cosine to calculate the forces on beams and supports at different angles.