trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. The tangent of half an angle is...

In integral calculus, the tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of...

trigonometric identities Prosthaphaeresis Pythagorean theorem Tangent half-angle formula Trigonometric number Trigonometry Uses of trigonometry Versine...

(see tangent half-angle formula). The law of tangents can be used to compute the angles of a triangle in which two sides a and b and the enclosed angle γ...

{x^{2}+y^{2}}}+x}}={\frac {\textstyle {\sqrt {x^{2}+y^{2}}}-x}{y}}.} (See tangent half-angle formula.) The expression with ⁠ y {\displaystyle y} ⁠ in the denominator...

difference formulas allow expanding the sine, the cosine, and the tangent of a sum or a difference of two angles in terms of sines and cosines and tangents of...

Plimpton 322 Pythagorean prime Pythagorean quadruple Quadric Tangent half-angle formula Trigonometric identity Long (1972, p. 48) Robson, Eleanor (2002)...

the angle between the x-axis and the major axis of the ellipse. Both parameterizations may be made rational by using the tangent half-angle formula and...

The expressions for n = 16 are obtained by twice applying the tangent half-angle formula to tan(π/4) Hwa, Young Lee (2017). Origami-Constructible Numbers...

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at...

identity Tangent half-angle formula Solution of triangles Law of sines Law of cosines Law of tangents Law of cotangents Mollweide's formula Chebyshev...

{n+{\sqrt {n^{2}+4}}}{2}}=e^{\operatorname {arsinh(n/2)} }.} A tangent half-angle formula gives cot ⁡ θ = cot 2 ⁡ θ 2 − 1 2 cot ⁡ θ 2 {\displaystyle \cot...

hemisphere. A tangent ogive nose is often blunted by capping it with a segment of a sphere. The tangency point where the sphere meets the tangent ogive can...

curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term angle is also used for the size, magnitude...

K_{\text{tri}}=((B+A)\times H)-(A\times H)=B\times H.} Another area formula, for two sides B and C and angle θ, is K = B ⋅ C ⋅ sin ⁡ θ . {\displaystyle K=B\cdot C\cdot...

In the diagram, such a circle is tangent to the hyperbola xy = 1 at (1,1). The yellow sector depicts an area and angle magnitude. Similarly, the yellow...

= 1 {\displaystyle A(0)=A_{0}/0!=1} ), and simplified using a tangent half-angle formula, giving the final result A ( x ) = tan ⁡ ( π 4 + x 2 ) = sec ⁡...

Mathematics, 5th edition, page 611, Wiley ISBN 0471862517 See Tangent half-angle formula Gallier, Jean (2006). "Remarks on the Cayley Representation of...

AF2 = AC × AD (tangent–secant theorem). The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the...

presents the values of sine, cosine, tangent, and other trigonometric functions for various angles. These angles are usually arranged across the top row...

is known as the Weierstrass substitution, which makes use of tangent half-angle formulas. For example, ∫ 4 cos ⁡ x ( 1 + cos ⁡ x ) 3 d x = ∫ 2 1 + u 2...

interior angle A that is opposite the side of length a. Using tangent half-angle formulas, it follows immediately that α = sin ⁡ ( A ) = 2 r 1 + r 2  and ...

diagram show that the tangent BE bisects the angle ∠FEC. In other words, the tangent to the parabola at any point bisects the angle between the lines joining...

} The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent...

median through the right-angled vertex is a radius, and the circumradius is half the length of the hypotenuse. The following formulas hold for the medians...

are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-". With these functions, one can...

equivalently, as the angle between the tangents of the great circle arcs where they meet at the vertex. Angles are expressed in radians. The angles of proper spherical...

cost-effective use of solar trackers. The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction...

of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios...

is not differentiable at the origin as it does not have a well defined tangent plane despite having well defined partial derivatives in every direction...