Understanding Terminal Point Ratios
A terminal point describes where a rotating vector ends after an angle starts at the positive x axis. In physics, that point can model force direction, velocity direction, phase position, or circular motion. The calculator converts the point into useful trigonometric ratios.
Why The Radius Matters
The radius is the distance from the origin to the terminal point. It is also the vector magnitude in many physics problems. When the radius is known, sine becomes vertical displacement divided by radius. Cosine becomes horizontal displacement divided by radius. Tangent compares vertical change with horizontal change. These ratios describe direction without needing the original path.
Signs And Quadrants
Signs are important because vectors point in different directions. A point in quadrant one gives positive sine, cosine, and tangent. Quadrant two gives positive sine, negative cosine, and negative tangent. Quadrant three gives negative sine, negative cosine, and positive tangent. Quadrant four gives negative sine, positive cosine, and negative tangent. The calculator reports these signs automatically.
Angle Interpretation
The angle is found with atan2, not simple inverse tangent. This matters because atan2 uses both coordinates and chooses the correct quadrant. The result is shown in degrees and radians. The reference angle is also shown. It is the acute angle between the terminal side and the nearest x axis.
Physics Use Cases
Terminal point ratios help resolve vectors into components. For example, a displacement vector with coordinates x and y has a direction angle, a magnitude, and normalized components. These values support work, torque, wave phase, oscillation, projectile motion, and circular motion tasks. The reciprocal ratios can also help when a formula uses secant, cosecant, or cotangent.
Practical Accuracy
Measurement inputs may come from drawings, sensors, simulations, or lab data. Rounding can change the final ratios, so the precision option is useful. The scale option helps when coordinates are entered from a graph image or drawing. The notes field stores extra context in the exported report.
Reporting Results
The export buttons are useful for homework records, lab sheets, and engineering notes. CSV files open in spreadsheet tools. PDF files provide a clean summary. The example table shows expected behavior across all quadrants. This supports quick checking before longer physics analysis work.