Part II: Trigonometry and geometry
What is trigonometry?
The word trigonometry consists of the Greek words tri for “three”, gono for “angle” and metron for “measure”. Trigonometry is based on the study of right triangles. It examines the relationships between the corners and sides of a triangle. It is based on the geometric fact that in a right triangle, the ratios of the lengths of the sides depend only on the magnitudes of the angles. The most important of these angle-determined ratios are sine, cosine and tangent. Calculating these numerical values is cumbersome, but they can also be obtained from tables or with a calculator.
Trigonometry evolved from the study of stars. Trigonometric functions have been used to solve a wide variety of geometric problems for more than 2,000 years. Trigonometric tables serving practical needs were compiled by the ancient Egyptians and Indians, but the relationships we use today was presented by Hipparchus around 150 BC.
Trigonometry has applications in technology, architecture, shipping and many other fields of practice. Trigonometry makes it possible to perform measurements that would otherwise be very cumbersome. These include measuring distances between objects in difficult terrain or at sea. Problems related to objects in air or in space can also be solved using trigonometric functions.
Trigonometric functions can be used to easily calculate the dimensions of other parts of the triangle based on its known parts. More complex patterns are calculated by first dividing them into suitable triangles. This is the case in astronomical calculations, where triangulation is based on the fact that when the angles of a triangle (the sum of which is always 180°) and the length of one side are known, the lengths of the other sides can be calculated. In practice, the angles are determined by aiming alternately at different points with a telescope-like device and looking at the angles of rotation from the scale plate of the telescope stand.
Trigonometric relations have proven to be important mathematical functions in many ways. They also play a key role in fairly abstract theories, such as in electrical engineering, radiation physics and information theory.
Trigonometry evolved from the study of stars. Trigonometric functions have been used to solve a wide variety of geometric problems for more than 2,000 years. Trigonometric tables serving practical needs were compiled by the ancient Egyptians and Indians, but the relationships we use today was presented by Hipparchus around 150 BC.
Trigonometry has applications in technology, architecture, shipping and many other fields of practice. Trigonometry makes it possible to perform measurements that would otherwise be very cumbersome. These include measuring distances between objects in difficult terrain or at sea. Problems related to objects in air or in space can also be solved using trigonometric functions.
Trigonometric functions can be used to easily calculate the dimensions of other parts of the triangle based on its known parts. More complex patterns are calculated by first dividing them into suitable triangles. This is the case in astronomical calculations, where triangulation is based on the fact that when the angles of a triangle (the sum of which is always 180°) and the length of one side are known, the lengths of the other sides can be calculated. In practice, the angles are determined by aiming alternately at different points with a telescope-like device and looking at the angles of rotation from the scale plate of the telescope stand.
Trigonometric relations have proven to be important mathematical functions in many ways. They also play a key role in fairly abstract theories, such as in electrical engineering, radiation physics and information theory.