Trigonometry Calculators
This category presents calculators describing angles, side lengths and trigonometric relationships. Each tool provides clear numerical outputs for right-angled and general triangles, covering core functions, their reciprocals and inverse operations.
-
Cosecant Calculator
The cosecant relationship grows larger as the sine value moves closer to zero, creating a repeating pattern of steep rises and falls across the angle scale.
Example use: Timing the height of a swing at a moment when it is close to its lowest point.
Inputs: angle
Outputs: angle in radians, sine value, cosecant value, reference angle, derivative, pythagorean identity
Visual: the cosecant curve with a marker showing the current angle and value
-
Cosine Calculator
The cosine relationship measures how far a point on a circular path lies along the horizontal direction as the angle increases.
Example use: Checking how far a rotating toy moves sideways at a particular moment.
Inputs: angle
Outputs: angle in radians, cosine value, reference angle, secant value
Visual: the cosine wave with a highlighted point for the chosen angle
-
Cotangent Calculator
The cotangent relationship compares the horizontal and vertical components of an angle, creating a repeating curve with sharp rises near its undefined points.
Example use: Estimating how steep a ramp appears when viewed from different angles.
Inputs: angle
Outputs: cotangent value, reciprocal of tangent, cofunction identity
Visual: the cotangent curve shown across one full cycle
-
Inverse Cosine (arccos) Calculator
The inverse cosine relationship gives the angle whose cosine matches a chosen horizontal value between negative one and one.
Example use: Working out the angle formed when a door is opened to a particular sideways position.
Inputs: x value
Outputs: arccos value, supplementary angle, reference angle
Visual: a set of arccos points on a curve with a matching arc on the unit circle
-
Inverse Sine (arcsin) Calculator
The inverse sine relationship returns the angle whose sine matches a chosen vertical value within the allowed range.
Example use: Checking the angle reached by a seesaw when one end rises to a certain height.
Inputs: x value
Outputs: angle in radians, angle in degrees, derivative, selected result
Visual: the arcsin curve with a point marking the chosen value
-
Inverse Tangent (arctan) Calculator
The inverse tangent relationship gives the angle whose tangent matches a chosen ratio of vertical to horizontal change.
Example use: Estimating the angle of a path when comparing how far it rises compared with how far it moves forward.
Inputs: x value
Outputs: arctan value, derivative at x
Visual: the arctan curve with its horizontal limits and a highlighted point
-
Law of Cosines Calculator
The law of cosines links the sides and angles of any triangle, allowing one side or angle to be determined when the others are known.
Example use: Working out the length between two corners of a garden when the connecting paths meet at a known angle.
Inputs: side a, angle a, side b, angle b, side c, angle c
Outputs: side lengths, angles, triangle type, semi-perimeter, area, circumradius
Visual: a triangle with its sides and angles labelled
-
Law of Sines Calculator
The law of sines relates each side of a triangle to the sine of its opposite angle, giving a consistent ratio across the whole shape.
Example use: Estimating the length of a rope stretched between two posts when the angle at one end is known.
Inputs: side a, angle a, side b, angle b, side c, angle c
Outputs: side lengths, angles, area, perimeter, inradius
Visual: a triangle showing its sides and opposite angles
-
Right Triangle Side and Angle Calculator
A right triangle has one angle fixed at ninety degrees, creating predictable relationships between its sides and remaining angles.
Example use: Checking the height of a ladder when its base is placed a certain distance from a wall.
Inputs: side a, side b, hypotenuse c, angle a, angle b
Outputs: side lengths, angles, perimeter, area, inradius, circumradius, altitude to hypotenuse
Visual: a right triangle with its inscribed and circumscribed circles shown
-
Secant Calculator
The secant relationship grows larger as the cosine value approaches zero, creating repeating peaks across the angle cycle.
Example use: Checking how sharply a rotating object moves away from the centre at a particular angle.
Inputs: angle
Outputs: cosine value, secant value, quadrant, reference angle, periodicity
Visual: the secant curve with markers showing the chosen angle
-
Sine Calculator
The sine relationship measures the vertical position of a point moving around a circle as the angle increases.
Example use: Estimating how high a rotating wheel lifts a point at a certain moment.
Inputs: angle
Outputs: radian equivalent, reference angle, cosecant value, sine value
Visual: the sine wave with a highlighted point for the chosen angle
-
Spherical Cap Angle Calculator
A spherical cap forms when a sphere is cut by a flat surface, creating a curved top whose angle depends on the height of the cut.
Example use: Estimating the curved top of a rounded bowl when filled to a certain height.
Inputs: sphere radius, cap height
Outputs: central angle, base radius, curved area, total area, volume, volume ratio, surface area ratio
Visual: a spherical cap with its height, base, and central angle shown
-
Tangent Calculator
The tangent relationship compares the vertical and horizontal components of an angle, producing a repeating curve with steep rises near its undefined points.
Example use: Estimating how steep a hill appears when comparing its rise to its forward distance.
Inputs: angle
Outputs: tangent value, sine value, cosine value, reference angle, quadrant, unit circle coordinates
Visual: the tangent curve with a marker showing the chosen angle
-
Trigonometric Identities Calculator
Trigonometric identities link the six main trigonometric relationships, showing how each value connects to the others across the angle cycle.
Example use: Checking how different angle relationships line up when comparing the height and sideways movement of a rotating point.
Inputs: angle
Outputs: sine, cosine, tangent, cotangent, secant, cosecant, quadrant, reference angle, pythagorean identity, cofunction identity, double-angle values, sum identity
Visual: sine and cosine waves alongside a unit circle with a reference triangle
Trigonometry Calculators FAQs
They generate results for sine, cosine and tangent, along with their reciprocal functions, inverse operations and various geometric rules used in triangle calculations.
The tools use trigonometric ratios, the Pythagorean theorem and the laws of sines and cosines to determine unknown side lengths.
Yes, results can be presented in either degrees or radians depending on the selected angle unit.
It refers to finding secant, cosecant or cotangent by taking the reciprocal of the primary sine, cosine or tangent ratios.