Trigonometry
Explore sin, cos, and tan on an interactive unit circle
About this calculator
Explore sine, cosine, and tangent on an interactive unit circle. Enter any angle to see its trig values plotted in real time. Ideal for students learning trigonometric functions and their relationships.
How to use the trigonometry calculator
- Pick direct mode (angle → ratio) or inverse mode (ratio → angle).
- Choose sin, cos, or tan from the function selector.
- Enter your input value in the selected unit (degrees or radians for direct, a ratio for inverse).
- Read the result and locate it on the interactive unit circle.
Common examples
- sin(30°) = 0.5
- cos(60°) = 0.5
- tan(45°) = 1
- sin(90°) = 1
- cos(0°) = 1
Frequently asked questions
What is the unit circle?
The unit circle is a circle of radius 1 centered at the origin. For an angle measured from the positive x-axis, the point on the unit circle has coordinates (cos θ, sin θ). The unit circle makes the relationships between sine, cosine, and tangent visible.
How do I switch between degrees and radians?
Use the angle unit selector. Degrees express a full turn as 360°; radians express it as 2π. 180° equals π radians. The same angle gives the same sine, cosine, and tangent values regardless of unit.
Why is tan(90°) undefined?
Tangent equals sine divided by cosine, and cos(90°) is 0. Dividing by zero is undefined, so tan(90°) — and tan of any odd multiple of 90° — has no real value. The calculator shows an explanatory state instead of a fake number.
What does inverse mode do?
Inverse mode takes a ratio (between −1 and 1 for arcsin/arccos, any real value for arctan) and returns the principal angle that produces it. The result respects the current angle unit setting.