Trigonometry
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, given some angles and side lengths, we can find some or all the others. For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC). 2. AnalyticallyIn a more advanced use, the trigonometric ratios such as as Sine and Tangent, are used as functions in equations and are manipulated using algebra. In this way, it has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, it deals with angles drawn on a coordinate plane, and can be used to analyze things like motion and waves. Chapter-1Angles in the Quadrants( Some basic Concepts)In trigonometry, an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along the positive x-axis.Names of the partsThe side that is fixed along the positive x axis (BC) is called the initial side. To make the angle, imagine of a copy of this side being rotated about the origin to create the second side, called the terminal side. The amount we rotate it is called the measure of the angle and is measured in degrees or radians. This measure can be written in a short form: mABC = 54° which is spoken as "the measure of angle ABC is 54 degrees". If it is not ambiguous, we may use just a single letter to denote an angle. In the figure
| 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, given some angles and side lengths, we can find some or all the others. For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC). 2. AnalyticallyIn a more advanced use, the trigonometric ratios such as as Sine and Tangent, are used as functions in equations and are manipulated using algebra. In this way, it has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, it deals with angles drawn on a coordinate plane, and can be used to analyze things like motion and waves. Chapter-1Angles in the Quadrants( Some basic Concepts)In trigonometry, an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along the positive x-axis.Names of the partsThe side that is fixed along the positive x axis (BC) is called the initial side. To make the angle, imagine of a copy of this side being rotated about the origin to create the second side, called the terminal side. The amount we rotate it is called the measure of the angle and is measured in degrees or radians. This measure can be written in a short form: mABC = 54° which is spoken as "the measure of angle ABC is 54 degrees". If it is not ambiguous, we may use just a single letter to denote an angle. In the figure