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Radius of the turn of leaning bike (for small steering angles)

This lean of the bike decreases the actual radius of the turn proportionally to the cosine of the lean angle. The resulting radius can be approximated ... more

Tangent of the difference of two angles (Bhāskara formula)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Tangent of the sum of two angles (Bhāskara formula)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Tangent of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Relation between inradius,exradii and sides of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

Relation between the inradius and exradii of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

Double-angle's cosine (related to the tangent)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Double-angle's sine (related to the tangent)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Spirograph (rotation angle of the inner circle)

Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
A ... more

Radius of the turn of an upright bike (for small steering angles)

In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any ... more

Secant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosecant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Law of tangents for the triangles

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.The law of ... more

Tangent Length (Horizontal curves for highway design)

Horizontal alignment in road design consists of straight sections of road, known as tangents, connected by circular horizontal curves. Circular curves are ... more

Spirograph (Y-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Spirograph (X-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Area of an arbitrary triangle (incircle and excircles)

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of ... more

Triple-angle's cosine (related to the cosine of the single angle)

rigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Triple-angle's sine (related to the sine of the single angle)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Bend Deduction - right angles

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Double angle's sine (related to the sine and cosine)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Double-angle's cosine( related to the cosine and the sine)

rigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Law of cotangents (in term of tangents)

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more

Tangent function

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

Bend allowance

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Area of a triangle (by the tangent of an acute or obtuse angle of the triangle)

A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. The area ... more

Sine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Tangential quadrilateral ( the sum of the opposite sides)

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose ... more

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