Drag the point or type an angle in degrees or radians and watch cosine, sine and tangent change as lengths on the circle. Special angles show exact values like √3/2.
| Function | Definition | Exact value | Decimal |
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cos and sin are the x and y of a point on the circle.
Exact values like √2/2 appear at 30°, 45°, 60° and their friends.
Watch signs change from one quadrant to the next.
The unit circle has radius 1 and its centre at the origin. Measuring an angle θ anticlockwise from the positive x-axis lands on a point P. The x-coordinate of P is cos θ and the y-coordinate is sin θ, which is why sin² θ + cos² θ = 1 for every angle.
The tangent is the length of the segment on the vertical line x = 1 cut off by the extended radius, which equals sin θ / cos θ and is undefined at 90° and 270°. The reference angle is the acute angle to the x-axis; its trig values are the same as the angle's, apart from the sign set by the quadrant.
All functions are positive.
sin is positive in II, tan in III, cos in IV.
180° = π rad, so 60° = π/3.
Choose Radians and type a decimal such as 1.047 or a multiple of pi such as pi/3, 2pi/3 or -3pi/4.
tan θ = sin θ / cos θ, and cos 90° = 0, so it would mean dividing by zero. The tangent line never meets the extended radius.
Multiples of 30° and 45°. Their sine and cosine values can be written exactly using 1/2, √2/2 and √3/2.
The acute angle between the terminal side and the x-axis. 150° has a reference angle of 30°.
Adding a full turn of 360° (2π) brings you back to the same point, so all trig functions are periodic.
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