SPHERICAL TRIGONOMETRY
DEFINITION OF TERMS
The sphere is the set of all points in a three-dimensional space such that the distance of each from a fixed point is constant. The fixed point and the given distance are called the center and the radius of the sphere respectively.

The intersection of a plane with a sphere is a circle. If the plane passes through the center of the sphere, the intersection is a great circle; otherwise, the intersection is a small circle.
A line perpendicular to the plane of a circle and through the center of the sphere is called the axis of the circle. The intersection of this axis and the sphere are called the poles of the circle. Opposite ends of a diameter are identified as antipodal points. Two great circles intersecting in a pair of antipodal points divide the sphere into four regions called lunes. Thus a lune is bounded by the arcs of two great circles.

The polar distance (in angular units) of a circle is the least distance of a point on the circle to its pole.
Two distinct points on the sphere which are not ends of a diameter divide the great circle into two arcs. The shorter arc is called the minor arc.

SPHERICAL TRIANGLES
A spherical triangle is that part of the surface of a sphere bounded by three arcs of great circles. The bounding arcs are called the sides of the spherical triangle and the intersections of these arcs are called the vertices of the spherical triangle. The angle formed by two intersecting arcs is called a spherical angle. Like a plane triangle, the spherical triangle has also six parts – three angles and three sides. The sides a, b, and c are measured by the corresponding faces of the trihedral angle. Important Propositions from Solid Geometry:

1. If two sides are equal, the angles opposite are equal and conversely. 2. If two sides are unequal, the angles opposite are unequal and the greater side is opposite the greater angle and conversely. 3. The sum of any two sides is...

...ENGTRIG: LECTURE # 4.2 SphericalTrigonometrySphericalTrigonometry
Engr. Christian Pangilinan
Areas of a Spherical Triangle
A=
π R2 E
180o E R
E = A + B + C − 180o
Where:
spherical excess radius of the sphere
Spherical Triangles Part of the surface of the sphere bounded by three arcs of three great circles Right Spherical Triangle – a...

...SphericaltrigonometrySphericaltrigonometry is that branch of spherical geometry which 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. Sphericaltrigonometry is of great importance for calculations in...

...Early trigonometry
The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all...

...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical...

...The Way Trigonometry is used in Astronomy
By: Joanna Matthews
Practical Applications of Advanced Mathematics
Mrs. Amy Goodrum
July 15, 2003
Abstract
This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas, such as engineering, chemistry, surveying, and physics, it is mainly used in astronomy Trigonometry is used to find the distance of stars, the distance from one planet to...

...MA1310 College Mathematics II LESSON PLAN WEEK 5
Dr. Tonjes September 2011
LESSON: Oblique Triangles, Laws of Sines and Cosines
INTRODUCTION:
Student will demonstrate how to apply laws of sines and cosines to oblique triangles.
OBJECTIVES:
After completing this unit, the student will be able to:
6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems.
6.1. Summarize the Law of Sines.
6.2. Find the area of an oblique triangle using the sine...

...CERAE
CHAPTER 6 CIRCULAR FUNCTIONS AND TRIGONOMETRY
CONTENTS
-Angles and Their Measures
-Degrees and Radians
-Angles in Standard Position and Coterminal Angles
-Angles in a Quadrant
-The Unit Circle
-Coordinates of Points on the Unit Circle
-The Sine and Cosine Function
-Values of Sine and Cosine Functions
-Graphs of Sine and Cosine Functions
-The Tangent Function
-Graph of Tangent Function
-Trigonometric Identities
-Sum and Difference of Formulas for Sine and...

...Trigonometry
| Introduction to trigonometryAs you see, the word itself refers to three angles - a reference to triangles. Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used: 1. In geometryIn its geometry application, it is mainly used to solve triangles, usually right triangles. That is,...