![]() The two main aims in this study are: 1) How the unit circle is used for drawing trigonometric function graph, 2) How the trigonometric function graph can be used to analyse the trigonometric function properties. We used the trigonometric function graph as a media to analyse the function such as trigonometric value, maximum and minimum, period, and interval in which it decreases or increases. Starting from drawing the graph then analyse each of the graphs. In this study, we propose a didactical design with the aim to figure out the properties of trigonometric functions. This is a qualitative study which elaborated the didactical design and the class observation of high school student. Thus, the competency in trigonometric function is an issue need further discussion. On the other hand, An understanding of trigonometric function is an initial stage in understanding calculus derived from it such as limit, derivative, and integral. Another finding from structured instructional designs is that working in groups allows students to share experiences more effectively.Ī Trigonometric function is one of the challenging materials for not only high school students but also pre-service teachers and teachers. The research results on how to analyze the results of the implementation of structured learning designs provide information that educators can use, including the use of graphing calculators to help and make it easier for students to identify graphs more quickly and make students accustomed to using trigonometric function symbols. The result of this research is a learning design that has been tested on 65 high school students. ![]() The worksheets were constructed based on the following focus areas: behaviour of graphs, constructing related-angle formula, and overall performance of the learner. Data were collected by using two trigonometry worksheets and lesson observations. This study is research on developing learning designs within the Didactical Design Research (DDR) framework presented in an exploratory narrative. The main objective of this study is to present classroom activities enriched with graphing calculators and observe responses about teaching with this approach. A total of 65 students were divided into two classes, the first class consisted of 32 students, and the second class consisted of 33 students. A sine wave is the mirror image of a cosine wave.This study explored the activitiesusing a graphing calculator of 10th-grade high school students on the trigonometry topic. For example sound and light waves, day length and temperature variations over the year can be represented as a sine.Ībove: a wave generated using the sine function. The sine function is usually used to model periodic phenomena in physics, biology, social sciences, etc. Other ways involve using the law of sines. For example, if sin(α) is to be computed and the lengths of a and c are available, sin(α) = a / c. If the angle itself is unknown, one way to calculate the sine is to know the measurements of the lengths of the side opposite to it as well as the hypotenuse (side c in the figure). Once you have measured the angle, or looked up the plan or schematic, just input the measurement and press "calculate". If the angle is known, then simply use our sine calculator which supports input in both degrees and radians. ![]() It is useful for finding an angle x when sin(x) is known. The arcsine function is multivalued, e.g. The inverse of the sine is the arcsine function: asin(x) or arcsin(x). The reciprocal of sine is the cosecant: csc(x), sometimes written as cosec(x), which gives the ratio of the length of the hypotenuse to the length of the side opposite to the angle. Other definitions express sines as infinite series or as differential equations, meaning a sine can be an arbitrary positive or negative value, or a complex number. The sine function can be extended to any real value based on the length of a certain line segment in a unit circle (circle of radius one, centered at the origin (0,0) of a Cartesian coordinate system. You can use this sine calculator to verify this.Ī commonly used law in trigonometry which is trivially derived from the sine definition is the law of sines: Since for a right triangle the longest side is the hypotenuse and it is opposite to the right angle, the sine of a right angle is equal to the ratio of the hypotenuse to itself, thus equal to 1. The function takes negative values for angles larger than 180°. In the illustration below, sin(α) = a/c and sin(β) = b/c.įrom cos(α) = a/c follows that the sine of any angle is always less than or equal to one. The sine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the opposite side to the longest side of the triangle. ![]()
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