What is the formula of spherical triangle?

What is the formula of spherical triangle?

Theorem: The area of spherical triangle △ABC is A + B + C − π. This quantity, A + B + C − π is called the excess. It’s amazing that the area has such a nice formula, depending only on the angles of the triangle!

What is spherical triangle properties?

A spherical triangle is a triangle each of whose sides is a great circle . The three angles of a spherical triangle must together be more than 180° and less than 540° . 7. The greater side is opposite the greater angle , if tow sides are equal their opposite angles are equal .

How many degrees are in a spherical triangle?

The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere’s surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

What is Napier’s formula?

For example, if we start with a, the first rule says sin a = cot B tan b. (The tangent of the complementary angle to B is the cotangent of B.) Similarly, the second rule says that sin a = sin c sin A. (The cosine of the complementary angle is just the sine.)

Who is the father of spherical trigonometry?

Nasīr al-Dīn al-Tūsī
In the 13th century, Nasīr al-Dīn al-Tūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form.

Who is Father of spherical trigonometry?

What is Napier’s rule?

: either of two rules in spherical trigonometry: the sine of any part is equal to the product of the tangents of the adjacent parts and the sine of any part is equal to the product of the cosines of the opposite parts.

What is Quadrantal triangle?

: a spherical triangle with one side equal to a quadrant.

Who found trigonometry?

Trigonometry in the modern sense began with the Greeks. Hipparchus (c. 190–120 bce) was the first to construct a table of values for a trigonometric function.

How are the sides of a spherical triangle related?

The mathematical discipline that studies the interdependence of the sides and angles of spherical triangles (see Spherical geometry ). Let A, B, C be the angles and let a, b, c be the opposite sides of a spherical triangle A B C . The angles and sides of the spherical triangle are related by the following basic formulas of spherical trigonometry:

Which is the positive quantity of a spherical triangle?

The positive quantity E = α + β + γ – 180° is called the spherical excess of the triangle. Since the sides of a spherical triangle are arcs, they can be described as angles, and so we have two kinds of angles:

What do you need to know about spherical trigonometry?

Spherical trigonometry. Jump to navigation Jump to search. Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

Are there any recent texts on spherical geometry?

This lack of recent texts on spherical geometry and trigonometry is puzzling because the use of computers should shift the emphasis from numerical computation to theory. This page is an attempt to present derivations of important results from spherical geometry and trigonometry.