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...

interior angle A that is opposite the side of length a. Using tangent half-angle formulas, it follows immediately that α = sin A = 2r / (1 + r2) and β...

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...

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) ⁠ 15 8 ( 15 + 3 + 2 ( 5 + 5 ) ) {\displaystyle {\tfrac...

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)...

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

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

define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. The magnitude of an angle is called...

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

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...

(}(1+x)/(1-x){\bigr )}} is the inverse hyperbolic tangent. This 2 arsinh {\textstyle 2\operatorname {arsinh} } formula can be thought of as coming from the chord...

trigonometry. In particular, the sine, cosine, and tangent functions relate side lengths and angles in right triangles. A triangle is a figure consisting...

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...

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...

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

{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...

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...

= 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 ⁡...

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...

(also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides...

triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of...

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...

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...

{1}{2}}(\alpha -\beta )}}.\end{aligned}}} In terms of half-angle tangents alone, Mollweide's formula can be written as a + b c = 1 + tan ⁡ 1 2 α tan ⁡ 1...