A terminal point is found by moving from the origin at angle θ for distance r. Cosine gives the horizontal coordinate and sine gives the vertical coordinate.
⚠Angle is entered in degrees and radius must be positive. Radius 1 gives the unit circle point.
How Terminal Points Work
The angle sets the direction and the radius sets the distance from the origin. Together they define a point in the coordinate plane.
Angle
Sets the direction from the x-axis.
Radius
Sets distance from the origin.
x Coordinate
x = r cos θ.
y Coordinate
y = r sin θ.
💡 Example: For θ=60° and r=5, the terminal point is approximately (2.5, 4.330127).
Applications of Terminal Points
Polar CoordinatesVectorsRotationsUnit Circle
Frequently Asked Questions
What is a terminal point calculator?▼
It finds the coordinate point reached by an angle and radius from the origin.
What is the terminal point formula?▼
The formula is x = r cos θ and y = r sin θ.
How do I use this calculator?▼
Enter the angle in degrees and the radius, then click Calculate.
Is this the same as the unit circle?▼
It matches the unit circle when radius is 1. Other radii scale the point.
Where are terminal points used?▼
They are used in polar coordinates, rotations, unit circle problems, vectors, and geometry.
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