Trigonometry Nodes
Sine, cosine, tangent, their inverses, and the hyperbolic functions, for numbers and vectors.
This category contains 26 nodes.
Nodes
Arccosine
Finds the angle whose cosine equals the input. It reverses Cosine.
Inputs: A value between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | ±1 | 0 |
Outputs: The angle in radians.
| Name | Type | Range |
|---|---|---|
| Number | Number | rad |
Arccosine Vector
Finds the angle whose cosine matches each component. It reverses Cosine Vector.
Inputs: A 3D vector with each component between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of angles.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Arcsine
Finds the angle whose sine equals the input. It reverses Sine.
Inputs: A value between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | ±1 | 0 |
Outputs: The angle in radians.
| Name | Type | Range |
|---|---|---|
| Number | Number | rad |
Arcsine Vector
Finds the angle whose sine matches each component. It reverses Sine Vector.
Inputs: A 3D vector with each component between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of angles.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Arctangent
Finds the angle whose tangent equals the input. It reverses Tangent.
Inputs: Any number.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | ±1 | 0 |
Outputs: The angle in radians.
| Name | Type | Range |
|---|---|---|
| Number | Number | rad |
Arctangent 2
Finds the angle from the origin to a point. Use it to turn an X and Y position into a rotation angle.
Inputs: The Y and X coordinates.
| Name | Type | Range | Default |
|---|---|---|---|
| Y | Number | ±1 | 0 |
| X | Number | ±1 | 1 |
Outputs: The angle in radians.
| Name | Type | Range |
|---|---|---|
| Number | Number | rad |
Arctangent 2 Vector
Finds the angle from each pair of Y and X components. Use it to turn positions into rotations.
Inputs: The Y and X vectors.
| Name | Type | Range | Default |
|---|---|---|---|
| Y | Vector | vec | [0, 0, 0] |
| X | Vector | vec | [1, 1, 1] |
Outputs: The vector of angles.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Arctangent Vector
Finds the angle whose tangent matches each component. It reverses Tangent Vector.
Inputs: A 3D vector.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of angles.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Cosine
Creates a smooth wave from an angle in radians. The wave is Sine shifted by a quarter cycle, so it starts at 1. To drive a wave from beat or bar progress without the tau multiply, use Oscillate with a phase offset of 0.25.
Inputs: An angle in radians.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | rad | 0 |
Outputs: A value between -1 and 1.
| Name | Type | Range |
|---|---|---|
| Number | Number | ±1 |
Cosine Vector
Applies a cosine wave to each component separately. It is Sine Vector shifted by a quarter cycle.
Inputs: A 3D vector of angles.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of wave values, each -1 to 1.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | ±1 |
Hyperbolic Cosine
Creates a catenary (hanging chain) curve. The result is always 1 or greater.
Inputs: Any number.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 0 |
Outputs: The result, always 1 or greater.
| Name | Type | Range |
|---|---|---|
| Number | Number | any |
Hyperbolic Cosine Vector
Applies hyperbolic cosine to each component to make catenary curves.
Inputs: A 3D vector.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of curved values, all 1 or greater.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Hyperbolic Sine
Creates an S-shaped curve that grows exponentially. Use it for asymmetric easing.
Inputs: Any number.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 0 |
Outputs: The result, which is unbounded and grows fast.
| Name | Type | Range |
|---|---|---|
| Number | Number | any |
Hyperbolic Sine Vector
Applies hyperbolic sine to each component, for S-shaped curves that grow exponentially.
Inputs: A 3D vector.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of curved values.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Hyperbolic Tangent
Squashes any value into the -1 to 1 range along a smooth S-curve. Use it for soft limiting.
Inputs: Any number.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 0 |
Outputs: A value between -1 and 1.
| Name | Type | Range |
|---|---|---|
| Number | Number | ±1 |
Hyperbolic Tangent Vector
Squashes each component into the -1 to 1 range along a smooth S-curve.
Inputs: A 3D vector.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of limited values, each -1 to 1.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | ±1 |
Inverse Hyperbolic Cosine
Returns the inverse of hyperbolic cosine. It takes values of 1 or greater and returns a compressed result.
Inputs: A value of 1 or greater.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 1 |
Outputs: The compressed result, always positive.
| Name | Type | Range |
|---|---|---|
| Number | Number | any |
Inverse Hyperbolic Cosine Vector
Applies the inverse of hyperbolic cosine to each axis. Each value must be 1 or greater.
Inputs: A 3D vector with values of 1 or greater.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [1, 1, 1] |
Outputs: The vector of inverse hyperbolic cosine values.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Inverse Hyperbolic Sine
Returns the inverse of hyperbolic sine. It compresses large values and keeps small values linear.
Inputs: Any number.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 0 |
Outputs: The compressed result.
| Name | Type | Range |
|---|---|---|
| Number | Number | any |
Inverse Hyperbolic Sine Vector
Applies the inverse of hyperbolic sine to each axis. Use it to compress values that hyperbolic sine expanded.
Inputs: A 3D vector.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of inverse hyperbolic sine values.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Inverse Hyperbolic Tangent
Returns the inverse of hyperbolic tangent. It stretches values near -1 and 1 toward very large magnitudes.
Inputs: A value between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | any | 0 |
Outputs: The expanded result, which can be very large.
| Name | Type | Range |
|---|---|---|
| Number | Number | any |
Inverse Hyperbolic Tangent Vector
Applies the inverse of hyperbolic tangent to each axis. It expands values out of the -1 to 1 range.
Inputs: A 3D vector with values between -1 and 1.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of expanded values.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |
Sine
Creates a smooth wave from an angle in radians, where one full cycle is 6.283. To drive a wave from beat or bar progress without the tau multiply, use Oscillate. Oscillate takes its phase in turns.
Inputs: An angle in radians.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | rad | 0 |
Outputs: A value between -1 and 1.
| Name | Type | Range |
|---|---|---|
| Number | Number | ±1 |
Sine Vector
Applies a sine wave to each component separately. Use it for oscillations on several axes.
Inputs: A 3D vector of angles.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of wave values, each -1 to 1.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | ±1 |
Tangent
Returns the ratio of sine to cosine. Its values spike to infinity at certain angles.
Inputs: An angle in radians.
| Name | Type | Range | Default |
|---|---|---|---|
| Value | Number | rad | 0 |
Outputs: The tangent, which can be very large.
| Name | Type | Range |
|---|---|---|
| Number | Number | ±1 |
Tangent Vector
Applies tangent to each component. The values spike at certain angles.
Inputs: A 3D vector of angles.
| Name | Type | Range | Default |
|---|---|---|---|
| Vector | Vector | vec | [0, 0, 0] |
Outputs: The vector of tangent values.
| Name | Type | Range |
|---|---|---|
| Vector | Vector | vec |