# Trigonometry for Rotation and Layout

Use sine, cosine, tangent, radians, and atan2 to turn angles into positions, rotations, slopes, and repeatable layout checks.

## Outcome
Move between an angle, a side length, and a coordinate change without guessing.

## Safe first step
Write whether the angle is in degrees or radians before using it in code, calculators, or sketches.

## Ladder steps
### 1. Name the triangle or circle
Trig answers a relationship between angle and length, so start with the shape.

Check: The sketch shows the angle and the known side or radius.

### 2. Choose the right function
Sine, cosine, tangent, and atan2 answer different questions.

Check: You can say which unknown each function is solving.

### 3. Respect radians and degrees
Game engines and math libraries often use radians while people describe angles in degrees.

Check: Your note names the unit before calculation.

### 4. Check the quadrant
atan2 keeps sign information that plain atan can lose.

Check: The result points in the expected direction on the drawing.

## Examples
### Place a point around a circle
```sh
x = cos(angle) * radius; y = sin(angle) * radius
```
Expected signal: The point moves around the origin at the chosen radius

### Find the angle from one point to another
```sh
angle = atan2(target_y - y, target_x - x)
```
Expected signal: The angle points from the current point to the target

### Estimate rise from angle and run
```sh
rise = tan(angle) * run
```
Expected signal: The computed rise matches the sketched slope direction

## Common traps
- Feeding degrees into a function that expects radians.
- Using atan when atan2 is needed.
- Trying to memorize identities before drawing the actual project shape.

## Practice task
Draw a rotating pointer, mark radius and angle, then compute where the tip should be for one simple angle.

## Next steps
- Use vectors if the project starts from points instead of angles.
- Use transformations when several rotations or translations combine.
- Use construction layout math for physical triangles.

## Related
- [Vectors for maker projects](/learn/vectors-for-maker-projects/)
- [Godot first playable loop](/learn/godot-first-playable-loop/)
- [Maker Math](/topics/math/)
- [Fabrication and materials](/topics/fabrication/)

## Obsidian backlinks

Use these wiki links to connect this note inside a local maker vault:

- [[TopicLadder]]
- [[Maker Learning]]
- [[Trigonometry for Rotation and Layout]]
- [[Maker Math]]
- [[math]]
- [[applied-foundation]]
- [[Name the triangle or circle]]
- [[Choose the right function]]
- [[Respect radians and degrees]]
- [[Check the quadrant]]
- [[Vectors for maker projects]]
- [[Godot first playable loop]]

## Source and next routes

Source: https://topicladder.com/learn/trigonometry-for-rotation-and-layout/

- [Vectors for maker projects](/learn/vectors-for-maker-projects/)
- [Godot first playable loop](/learn/godot-first-playable-loop/)
- [Maker Math](/topics/math/)
- [Fabrication and materials](/topics/fabrication/)