The Concept of Trigonometry
Question :
Reflect on the concepts of trigonometry. What concepts (only the names) did you need to accommodate the concepts of trigonometry in your mind? What are the simplest trigonometry concepts you can imagine? In your day to day, is there any occurring fact that can be interpreted as periodic patterns? What strategy are you using to get the graphs of trigonometric functions?
Answer :
The concept of trigonometry
Trigonometry is referred to as a brand of mathematics in which students learn or study about particular functions of angles as well as their application to calculations. There are six commonly used functions of angles in trigonometry such as Sine as known and written as sin, cosine (cos), tangent (tan), cotangent (cot), secant (sec), as well as cosecant (cosec). The concept of trigonometry developed from the need for computing distance and angle in the following fields such as astronomy, surveying, mapmaking, artillery, etc. The concept of trigonometry can be categorized into two such as plane trigonometry and spherical trigonometry (Lial, 2016). Plane trigonometry covers the problems which involve angles as well as distance in one plane. On the other hand, spherical trigonometry covers the application of similar problems in more than one plane of three-dimensional space. A triangle consists of three sides such as the bottom side, perpendicular, and diagonal side. The bottom side is commonly known as base and denoted as (b), perpendicular is called height and denoted as (h), while the diagonal side is called hypotenuse and denoted as (l). With the help of these, the core geometrical concept is can be derived. The core geometrical concept is (hypotenuse)2 = (base)2 + (height)2 or l2 = b2 + h2.
In order to accommodate the concept of trigonometry, the concept of the Pythagoras Theorem can be used.
Simplest trigonometry concept
The simplest trigonometry concept describes trigonometry as the study of triangles. It is a system that deals with triangles and with the help of this concept we can easily work out the missing angle.
Occurring facts that can be interpreted as a periodic pattern
Yes, there are several examples of occurring fact which can be interpreted as a periodic pattern such as the motion of swing of children is periodic (McKeague and Turner, 2016). An individual walks every day for 30 minutes as a physical exercise is also a periodic pattern.
Strategy to get the graph of trigonometry functions
The following strategy can be used to get the graphs of trigonometric functions.
• The first step of graphing a trigonometry function is to find the value for range and domain.
• After finding the value for range and domain, there is a need to calculate the x-intercept of the graph
• Then calculate the minimum and maximum points of the graph
• After finding the minimum and maximum points of the graph, denote the points on the graph and sketch the graph of the function.
References
Lial, M. L. (2016). College algebra and trigonometry. Pearson Education.
McKeague, C. P., & Turner, M. D. (2016). Trigonometry. Cengage Learning.
